Finite Group Databasebeta

← C2×#80128 #11670204

Subgroups — C2×#80128 #11670204

Order 768.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5829C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C22×#911C211yesmaximal, characteristic, complemented
4C2×#5599C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic, complemented
6C2×#5173C211yesmaximal, characteristic, complemented
7C2×#5176C211yesmaximal, characteristic, complemented
8C2×#5150C211yesmaximal, characteristic, complemented
9C2×#5038C211yesmaximal, characteristic, complemented
10#80128C2116yesmaximal, direct product factor
11C2×#4798C211yesmaximal, characteristic, complemented
12C2×#4812C211yesmaximal, characteristic, complemented
13C2×#4773C211yesmaximal, characteristic, complemented
14C2×#4757C211yesmaximal, characteristic, complemented
15C2×#4734C211yesmaximal, characteristic, complemented
16C2×#4730C211yesmaximal, characteristic, complemented
17C2×#3268—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×#237C2211yescharacteristic
20C22×D3×D4C2211yescharacteristic
21C22×#235C2211yescharacteristic, complemented
22C22×C3×SD16C2211yescharacteristic, complemented
23C22×C3×D8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic, complemented
25#5829—24no—
26#5829C2218yescomplemented
27C2×#950—28no—
28C2×#950C2218yescomplemented
29C2×#947C2211yescharacteristic
30C2×#946C2211yescharacteristic
31C22×#216C2211yescharacteristic, complemented
32C22×#215C2211yescharacteristic, complemented
33C2×#940—21no—
34C2×#940C2211yescharacteristic, complemented
35C2×#939—21no—
36C2×#939—21no—
37C2×#937—21no—
38C2×D4×Dic3C2211yescharacteristic
39C22×#214C2211yescharacteristic
40C22×#213C2211yescharacteristic
41C22×#213C2211yescharacteristic
42C2×#930C2211yescharacteristic
43C2×#929—21no—
44C2×C4×#67C2211yescharacteristic
45C22×(C2×D3)⋊C4—21no—
46C23×C3⋊C8C2211yescharacteristic, complemented
47C2×#911—28no—
48C2×#911C2218yescomplemented
49C22×D24C2211yescharacteristic
50C22×#204C2211yescharacteristic
51C22×ΓL(1,𝔽25)C2211yescharacteristic
52#5599—24no—
53#5599C2218yescomplemented
54C2×#895C2211yescharacteristic
55C2×#887C2211yescharacteristic, complemented
56C2×#884—21no—
57C2×#67⋊C4—21no—
58C3×#449C2218yescomplemented
59C2×C3×#103C2211yescharacteristic, complemented
60C2×C3×#102C2211yescharacteristic
61C2×C3×C22⋊C8C2211yescharacteristic, complemented
62C2×#832C2211yescharacteristic, complemented
63#5176C2218yescomplemented
64#5173C2218yescomplemented
65#5150C2218yescomplemented
66C2×#821C2211yescharacteristic, complemented
67C2×(C2×D3)⋊C8C2211yescharacteristic
68C2×#816C2211yescharacteristic, complemented
69C2×#815C2211yescharacteristic, complemented
70C2×Dic3⋊C8C2211yescharacteristic, complemented
71#5038C2218yescomplemented
72C2×#809C2211yescharacteristic
73C2×#807C2211yescharacteristic, complemented
74#4812C2218yescomplemented
75#4798C2218yescomplemented
76#4773C2218yescomplemented
77#4757C2218yescomplemented
78#4734C2218yescomplemented
79#4730C2218yescomplemented
80C22×AGL(1,ℤ/8)—31no—
81C22×#135—31no—
82C2×#550—31no—
83C2×#546—31no—
84#3268—316no—
85C2×#496—31no—
86C2×#468—31no—
87C2×#466—31no—
88C2×#464—31no—
89C2×#459—31no—
90C2×#452—31no—
91C2×#449—31no—
92C2×#449D311yescharacteristic, complemented
93C2×#447—31no—
94C2×#440—31no—
95C2×#435—31no—
96C24×D3—21no—
97C2×C3×#41—22no—
98C2×C3×#41—24no—
99C2×C3×#41—42no—
100C2×C3×#41C2314yes—
101C22×C3×Q8C2311yescharacteristic
102C22×C3×D4—21no—
103C22×C3×D4—21no—
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4—21no—
107C23×C3×C4C2311yescharacteristic
108C22×#67—21no—
109C22×#67—21no—
110C22×#67—21no—
111C22×#67—21no—
112C22×#67—21no—
113C22×#67—21no—
114C22×#67D411yescharacteristic
115C23×Dic3—21no—
116C23×Dic3—21no—
117C2×#237—22no—
118C2×#237—24no—
119C2×#237—42no—
120C2×#237C2314yes—
121C2×D3×D4—24no—
122C2×D3×D4—22no—
123C2×D3×D4—42no—
124C2×D3×D4C2314yes—
125C2×#235—22no—
126C2×#235—24no—
127C2×#235—42no—
128C2×#235C2314yescomplemented
129C22×D12—21no—
130C22×D12C2311yescharacteristic
131C22×D12C2311yescharacteristic
132C22×C4×D3—21no—
133C22×C4×D3C2311yescharacteristic
134C22×Dic6C2311yescharacteristic
135C2×C3×SD16—42no—
136C2×C3×SD16C2314yescomplemented
137C2×C3×D8—24no—
138C2×C3×D8C2314yes—
139C22×C3×C8C2311yescharacteristic
140C22×C3×C8C2311yescharacteristic
141C3×#121—22no—
142C3×#121C2314yescomplemented
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C22⋊C4—21no—
145C2×#217—21no—
146C2×#217D411yescharacteristic
147#950—232no—
148#947—22no—
149#947C2314yes—
150#946—22no—
151#946C2314yes—
152C2×#216—24no—
153C2×#216C2314yescomplemented
154C2×#215—24no—
155C2×#215C2314yescomplemented
156#940—28no—
157#940—22no—
158#940C2314yescomplemented
159#939—28no—
160#939—28no—
161#937—28no—
162D4×Dic3—22no—
163D4×Dic3C2314yes—
164C2×#214D418yescomplemented
165C2×#214C2314yes—
166C2×#213—24no—
167C2×#213—24no—
168C2×#213C2314yes—
169C2×#213C2314yes—
170#930—22no—
171#930C2314yes—
172#929—28no—
173C4×#67D414yes—
174C4×#67C2314yes—
175C2×(C2×D3)⋊C4—21no—
176C2×(C2×D3)⋊C4—21no—
177C2×(C2×D3)⋊C4—21no—
178C2×(C2×D3)⋊C4—21no—
179C2×(C2×D3)⋊C4—21no—
180C2×(C2×D3)⋊C4—28no—
181C2×(C2×D3)⋊C4D411yescharacteristic
182C2×C4⋊Dic3C2311yescharacteristic
183C2×Dic3⋊C4—21no—
184C2×Dic3⋊C4—21no—
185C2×Dic3⋊C4D411yescharacteristic
186C2×C4×Dic3—21no—
187C2×C4×Dic3C2311yescharacteristic
188C22×C3⋊C8—24no—
189C22×C3⋊C8C2311yescharacteristic
190C22×C3⋊C8C2311yescharacteristic
191C22×C3⋊C8C2314yescomplemented
192#911—232no—
193C2×D24—42no—
194C2×D24C2314yes—
195C2×#204—24no—
196C2×#204C2314yes—
197C2×ΓL(1,𝔽25)—24no—
198C2×ΓL(1,𝔽25)C2314yes—
199#895—22no—
200#895C2314yes—
201#887—22no—
202#887C2314yescomplemented
203#884—28no—
204#67⋊C4—28no—
205C3×#103C2314yescomplemented
206C3×#102C2314yes—
207C3×C22⋊C8C2314yescomplemented
208#832C2314yescomplemented
209#821C2314yescomplemented
210(C2×D3)⋊C8C2314yes—
211#816C2314yescomplemented
212#815C2314yescomplemented
213Dic3⋊C8C2314yescomplemented
214#809C2314yes—
215#807C2314yescomplemented
216C22×#41—31no—
217C22×#41—31no—
218C22×#41C2×D311yescharacteristic
219C23×D4—31no—
220C2×AGL(1,ℤ/8)—38no—
221C2×AGL(1,ℤ/8)—68no—
222C2×#135—38no—
223C2×#135—68no—
224C22×Q16—31no—
225C22×SD16—31no—
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16C2×D311yescharacteristic, complemented
229C22×D8—31no—
230C22×D8—31no—
231C22×D8—31no—
232C22×D8C2×D311yescharacteristic
233C22×M16—31no—
234C23×C8—31no—
235#550—38no—
236#550—64no—
237#546—38no—
238#546—64no—
239C2×#127—31no—
240C2×#127—61no—
241C2×#124—31no—
242C2×#123—61no—
243C2×C22⋊Q8—31no—
244C2×#121—31no—
245C2×#121—31no—
246C2×#121—61no—
247C2×#121—61no—
248C2×#121—61no—
249C2×#121C2×D311yescharacteristic, complemented
250C2×#120—61no—
251C2×C4×Q8—31no—
252C2×C4×D4—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C22×C22⋊C4—61no—
256#496—38no—
257#468—38no—
258#466—38no—
259#464—38no—
260#459—38no—
261#452—38no—
262#449—38no—
263#449C2×D318yescomplemented
264#447—38no—
265#440—38no—
266#435—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103C2×D311yescharacteristic, complemented
271C2×#102—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102C2×D311yescharacteristic
275C2×C22⋊C8—31no—
276C2×C22⋊C8C2×D311yescharacteristic, complemented
277C2×#97—31no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3C2×D411yescharacteristic
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—24no—
284C23×D3—44no—
285C23×D3—44no—
286C23×D3—82no—
287C23×D3C2×D411yescharacteristic
288C3×#41—28no—
289C3×#41—44no—
290C3×#41—48no—
291C2×C3×Q8—21no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8C2412yes—
295C2×C3×D4—24no—
296C2×C3×D4—24no—
297C2×C3×D4—21no—
298C2×C3×D4—22no—
299C2×C3×D4—21no—
300C2×C3×D4—22no—
301C2×C3×D4—22no—
302C2×C3×D4—44no—
303C2×C3×D4—82no—
304C2×C3×D4C2×D414yes—
305C2×C3×D4C2412yes—
306C2×C3×D4C2412yes—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—24no—
312C22×C3×C4—44no—
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D412yes—
315C22×C3×C4C2412yes—
316C22×C3×C4C2411yescharacteristic
317C2×#67—24no—
318C2×#67—24no—
319C2×#67—24no—
320C2×#67—24no—
321C2×#67—24no—
322C2×#67—24no—
323C2×#67—42no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67—44no—
327C2×#67—44no—
328C2×#67—82no—
329C2×#67—82no—
330C2×#67C2×D414yes—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—24no—
334C22×Dic3—24no—
335C22×Dic3—44no—
336C22×Dic3—82no—
337C22×Dic3C2×D411yescharacteristic
338C22×Dic3C2×D411yescharacteristic
339C22×Dic3C2×D411yescharacteristic
340#237—28no—
341#237—44no—
342#237—48no—
343D3×D4—28no—
344D3×D4—44no—
345D3×D4—48no—
346#235—28no—
347#235—44no—
348#235—48no—
349C2×D12—22no—
350C2×D12—22no—
351C2×D12—22no—
352C2×D12—22no—
353C2×D12—21no—
354C2×D12—21no—
355C2×D12—24no—
356C2×D12—82no—
357C2×D12C2412yes—
358C2×D12C2412yes—
359C2×C4×D3—22no—
360C2×C4×D3—22no—
361C2×C4×D3—24no—
362C2×C4×D3—44no—
363C2×C4×D3C2×D412yes—
364C2×C4×D3C2412yes—
365C2×Dic6—21no—
366C2×Dic6—22no—
367C2×Dic6C2×D414yes—
368C2×Dic6C2412yes—
369C3×SD16—44no—
370C3×D8—28no—
371C2×C3×C8—22no—
372C2×C3×C8—22no—
373C2×C3×C8C2412yes—
374C2×C3×C8C2412yes—
375C3×C4⋊C4—21no—
376C3×C4⋊C4C2412yes—
377C3×C22⋊C4—24no—
378#217—24no—
379#217C2×D414yes—
380#216—28no—
381#215—28no—
382#214C2×D4116yescomplemented
383#213—28no—
384#213—28no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4—24no—
388(C2×D3)⋊C4—24no—
389(C2×D3)⋊C4—24no—
390(C2×D3)⋊C4C2×D414yes—
391C4⋊Dic3—21no—
392C4⋊Dic3C2412yes—
393Dic3⋊C4—24no—
394Dic3⋊C4—24no—
395Dic3⋊C4C2×D414yes—
396C4×Dic3—24no—
397C4×Dic3C2×D412yes—
398C4×Dic3C2412yes—
399C2×C3⋊C8—22no—
400C2×C3⋊C8—28no—
401C2×C3⋊C8C2×D414yes—
402C2×C3⋊C8C2412yes—
403C2×C3⋊C8C2412yes—
404D24—44no—
405#204—28no—
406ΓL(1,𝔽25)—28no—
407C25—61no—
408C2×#41—22no—
409C2×#41—24no—
410C2×#41—34no—
411C2×#41—34no—
412C2×#41—42no—
413C2×#41—64no—
414C2×#41—62no—
415C2×#41—62no—
416C2×#41—64no—
417C2×#41—122no—
418C2×#41—122no—
419C2×#41C22×D314yes—
420C22×Q8—31no—
421C22×Q8C22×D311yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—31no—
425C22×D4—34no—
426C22×D4—31no—
427C22×D4—31no—
428C22×D4—61no—
429C22×D4—62no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—64no—
434C22×D4—61no—
435C22×D4—61no—
436C22×D4—61no—
437C22×D4—122no—
438C22×D4C22×D311yescharacteristic
439C22×D4C22×D311yescharacteristic
440C23×C4—21no—
441C23×C4—31no—
442C23×C4—61no—
443C23×C4—61no—
444C23×C4—61no—
445C23×C4C22×D311yescharacteristic
446AGL(1,ℤ/8)—632no—
447#135—632no—
448C2×Q16—34no—
449C2×Q16—64no—
450C2×SD16—38no—
451C2×SD16—34no—
452C2×SD16—34no—
453C2×SD16—34no—
454C2×SD16—42no—
455C2×SD16—64no—
456C2×SD16—64no—
457C2×SD16C22×D314yescomplemented
458C2×D8—24no—
459C2×D8—34no—
460C2×D8—34no—
461C2×D8—34no—
462C2×D8—64no—
463C2×D8—64no—
464C2×D8—122no—
465C2×D8C22×D314yes—
466C2×M16—34no—
467C2×M16—64no—
468C22×C8—31no—
469C22×C8—31no—
470C22×C8—34no—
471C22×C8—64no—
472C22×C8C22×D311yescharacteristic
473C22×C8C22×D311yescharacteristic
474#127—34no—
475#127—62no—
476#127—68no—
477#124—34no—
478#124—62no—
479#123—68no—
480C22⋊Q8—34no—
481C22⋊Q8—62no—
482#121—22no—
483#121—34no—
484#121—34no—
485#121—68no—
486#121—68no—
487#121—68no—
488#121—62no—
489#121—62no—
490#121C22×D314yescomplemented
491#120—68no—
492C4×Q8—34no—
493C4×Q8—62no—
494C4×D4—34no—
495C4×D4—34no—
496C4×D4—34no—
497C4×D4—62no—
498C4×D4—68no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—61no—
502C2×C4⋊C4—61no—
503C2×C4⋊C4C22×D311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—68no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512C2×C22⋊C4—61no—
513C2×C22⋊C4—61no—
514C2×C42—31no—
515C2×C42—61no—
516#107—34no—
517C4⋊C8—34no—
518#103—34no—
519#103C22×D314yescomplemented
520#102—34no—
521#102—34no—
522#102—34no—
523#102C22×D314yes—
524C22⋊C8—34no—
525C22⋊C8C22×D314yescomplemented
526#97—34no—
527C23×C3—22no—
528C23×C3—24no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—42no—
534C23×C3—42no—
535C23×C3—42no—
536C23×C3—42no—
537C23×C3—42no—
538C23×C3C22×D412yes—
539C23×C3C22×D411yescharacteristic
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—48no—
546C22×D3—48no—
547C22×D3—42no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—84no—
554C22×D3—816no—
555C22×D3C22×D412yes—
556C3×Q8—22no—
557C3×Q8—22no—
558C3×Q8—42no—
559C3×D4—24no—
560C3×D4—22no—
561C3×D4—22no—
562C3×D4—22no—
563C3×D4—48no—
564C3×D4—42no—
565C3×D4—84no—
566C3×D4C22×D414yes—
567C2×C3×C4—22no—
568C2×C3×C4—24no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—48no—
574C2×C3×C4—42no—
575C2×C3×C4—42no—
576C2×C3×C4C22×D412yes—
577C2×C3×C4C22×D411yescharacteristic
578C2×C3×C4C22×D412yes—
579C2×C3×C4H(5,𝔽2)12yes—
580C2×C3×C4C2511yescharacteristic
581#67—44no—
582#67—48no—
583#67—48no—
584#67—48no—
585#67—48no—
586#67—84no—
587#67—84no—
588C2×Dic3—24no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—48no—
595C2×Dic3—42no—
596C2×Dic3—84no—
597C2×Dic3C22×D412yes—
598C2×Dic3C22×D412yes—
599C2×Dic3C22×D412yes—
600D12—22no—
601D12—22no—
602D12—22no—
603D12—22no—
604D12—42no—
605D12—42no—
606D12—84no—
607C4×D3—24no—
608C4×D3—22no—
609C4×D3—22no—
610C4×D3—48no—
611Dic6—24no—
612Dic6—22no—
613Dic6C22×D414yes—
614C3×C8—22no—
615C3×C8—22no—
616C3⋊C8—22no—
617C3⋊C8C22×D414yes—
618C24—21no—
619C24—21no—
620C24—31no—
621C24—64no—
622C24—61no—
623C24—61no—
624C24—124no—
625C24—124no—
626C24—242no—
627C24D3×D411yescharacteristic
628#41—28no—
629#41—44no—
630#41—48no—
631#41—68no—
632#41—68no—
633#41—124no—
634#41—128no—
635#41—124no—
636#41—128no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—34no—
641C2×Q8—32no—
642C2×Q8—61no—
643C2×Q8—62no—
644C2×Q8C23×D312yes—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—34no—
653C2×D4—32no—
654C2×D4—32no—
655C2×D4—44no—
656C2×D4—64no—
657C2×D4—64no—
658C2×D4—64no—
659C2×D4—64no—
660C2×D4—68no—
661C2×D4—64no—
662C2×D4—64no—
663C2×D4—64no—
664C2×D4—62no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—62no—
669C2×D4—62no—
670C2×D4—82no—
671C2×D4—124no—
672C2×D4—128no—
673C2×D4—122no—
674C2×D4—124no—
675C2×D4—124no—
676C2×D4—124no—
677C2×D4—124no—
678C2×D4—242no—
679C2×D4—242no—
680C2×D4—242no—
681C2×D4D3×D414yes—
682C2×D4C23×D312yes—
683C2×D4C23×D312yes—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—44no—
695C22×C4—64no—
696C22×C4—64no—
697C22×C4—61no—
698C22×C4—62no—
699C22×C4—62no—
700C22×C4—61no—
701C22×C4—64no—
702C22×C4—124no—
703C22×C4—124no—
704C22×C4—242no—
705C22×C4D3×D412yes—
706C22×C4D3×D411yescharacteristic
707C22×C4C23×D312yes—
708C22×C4C23×D311yescharacteristic
709Q16—68no—
710SD16—316no—
711SD16—44no—
712SD16—68no—
713SD16—68no—
714D8—28no—
715D8—68no—
716D8—68no—
717D8—124no—
718M16—68no—
719C2×C8—22no—
720C2×C8—22no—
721C2×C8—34no—
722C2×C8—32no—
723C2×C8—32no—
724C2×C8—68no—
725C2×C8—62no—
726C2×C8C23×D312yes—
727C2×C8C23×D312yes—
728C4⋊C4—21no—
729C4⋊C4—34no—
730C4⋊C4—32no—
731C4⋊C4—64no—
732C4⋊C4—64no—
733C4⋊C4—61no—
734C4⋊C4C23×D312yes—
735C22⋊C4—24no—
736C22⋊C4—34no—
737C22⋊C4—34no—
738C22⋊C4—64no—
739C22⋊C4—64no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C42—32no—
745C42—32no—
746C42—64no—
747C22×C3—22no—
748C22×C3—24no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—48no—
752C22×C3—44no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—84no—
759C22×C3D4212yes—
760C22×C3#57512yes—
761C22×C3#57612yes—
762C22×C3C23×D411yescharacteristic
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—44no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C2×D3—816no—
774C2×D3—84no—
775C2×D3—84no—
776C3×C4—22no—
777C3×C4—42no—
778C3×C4—42no—
779C3×C4D4212yes—
780C3×C4C23×D411yescharacteristic
781C3×C4C2×H(5,𝔽2)11yescharacteristic
782Dic3—24no—
783Dic3—22no—
784Dic3—22no—
785Dic3—22no—
786Dic3—42no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—24no—
792C23—22no—
793C23—32no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—128no—
805C23—128no—
806C23—122no—
807C23—122no—
808C23—122no—
809C23—122no—
810C23—122no—
811C23—122no—
812C23—244no—
813C23—2416no—
814C23C2×D3×D412yes—
815C23C2×D3×D411yescharacteristic
816Q8—22no—
817Q8—22no—
818Q8—34no—
819Q8—42no—
820Q8—62no—
821Q8—64no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—24no—
826D4—48no—
827D4—42no—
828D4—62no—
829D4—62no—
830D4—62no—
831D4—62no—
832D4—84no—
833D4—124no—
834D4—128no—
835D4—128no—
836D4—128no—
837D4—128no—
838D4—122no—
839D4—122no—
840D4—244no—
841D4—244no—
842D4—244no—
843D4C2×D3×D414yes—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—48no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—64no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—64no—
864C2×C4—62no—
865C2×C4—128no—
866C2×C4—128no—
867C2×C4—122no—
868C2×C4—244no—
869C2×C4C2×D3×D412yes—
870C2×C4C2×D3×D412yes—
871C2×C4C2×D3×D411yescharacteristic
872C2×C4#100412yes—
873C2×C4C24×D311yescharacteristic
874C8—22no—
875C8—22no—
876C8—34no—
877C8—62no—
878C2×C3—44no—
879C2×C3—42no—
880C2×C3—82no—
881C2×C3#326814yescomplemented
882C2×C3C2×D4211yescharacteristic
883C2×C3C2×#57511yescharacteristic
884C2×C3C2×#57611yescharacteristic
885D3—42no—
886D3—82no—
887D3—82no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—24no—
892C22—44no—
893C22—48no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—84no—
903C22—124no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—2416no—
911C22—244no—
912C22—244no—
913C22#559012yes—
914C22#576812yes—
915C22#577412yes—
916C22C22×D3×D411yescharacteristic
917C4—22no—
918C4—42no—
919C4—42no—
920C4—62no—
921C4—62no—
922C4—62no—
923C4—64no—
924C4—122no—
925C4#559012yes—
926C4C22×D3×D411yescharacteristic
927C4C2×#100411yescharacteristic
928C3C2×#326811yescharacteristic, complemented, Sylow
929C2—42no—
930C2—44no—
931C2—82no—
932C2—122no—
933C2—242no—
934C2—242no—
935C2#8012814yesdirect product factor
936C2C2×#559011yescharacteristic
937C2C2×#576811yescharacteristic
938C2C2×#577411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3C2×#3268
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5829C2semidirect
2. C22×#950C2semidirect
3. C22×#911C2semidirect
4. C2×#5599C2semidirect
5. C2×C3×#449C2semidirect
6. C2×#5173C2semidirect
7. C2×#5176C2semidirect
8. C2×#5150C2semidirect
9. C2×#5038C2semidirect
10. #80128C2direct (N × H)
11. C2×#4798C2semidirect
12. C2×#4812C2semidirect
13. C2×#4773C2semidirect
14. C2×#4757C2semidirect
15. C2×#4734C2semidirect
16. C2×#4730C2semidirect
21. C22×#235C22semidirect
22. C22×C3×SD16C22semidirect
24. C2×C3×#121C22semidirect
26. #5829C22semidirect
28. C2×#950C22semidirect
31. C22×#216C22semidirect
32. C22×#215C22semidirect
34. C2×#940C22semidirect
46. C23×C3⋊C8C22semidirect
48. C2×#911C22semidirect
53. #5599C22semidirect
55. C2×#887C22semidirect
58. C3×#449C22semidirect
59. C2×C3×#103C22semidirect
61. C2×C3×C22⋊C8C22semidirect
62. C2×#832C22semidirect
63. #5176C22semidirect
64. #5173C22semidirect
65. #5150C22semidirect
66. C2×#821C22semidirect
68. C2×#816C22semidirect
69. C2×#815C22semidirect
70. C2×Dic3⋊C8C22semidirect
71. #5038C22semidirect
73. C2×#807C22semidirect
74. #4812C22semidirect
75. #4798C22semidirect
76. #4773C22semidirect
77. #4757C22semidirect
78. #4734C22semidirect
79. #4730C22semidirect
92. C2×#449D3semidirect
128. C2×#235C23semidirect
136. C2×C3×SD16C23semidirect
142. C3×#121C23semidirect
153. C2×#216C23semidirect
155. C2×#215C23semidirect
158. #940C23semidirect
164. C2×#214D4semidirect
191. C22×C3⋊C8C23semidirect
202. #887C23semidirect
205. C3×#103C23semidirect
207. C3×C22⋊C8C23semidirect
208. #832C23semidirect
209. #821C23semidirect
211. #816C23semidirect
212. #815C23semidirect
213. Dic3⋊C8C23semidirect
215. #807C23semidirect
228. C22×SD16C2×D3semidirect
249. C2×#121C2×D3semidirect
263. #449C2×D3semidirect
270. C2×#103C2×D3semidirect
276. C2×C22⋊C8C2×D3semidirect
382. #214C2×D4semidirect
457. C2×SD16C22×D3semidirect
490. #121C22×D3semidirect
519. #103C22×D3semidirect
525. C22⋊C8C22×D3semidirect
881. C2×C3#3268semidirect
928. C3C2×#3268semidirect
935. C2#80128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58292
C22×#9502
C22×#9112
C2×#55992
C2×C3×#4492
C2×#51732
C2×#51762
C2×#51502
C2×#50382
#801282
C2×#47982
C2×#48122
C2×#47732
C2×#47572
C2×#47342
C2×#47302
C2×#32683