Finite Group Databasebeta

← C2×#83577 #11670201

Subgroups — C2×#83577 #11670201

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×C3×#550C211yesmaximal, characteristic, complemented
2C22×#949C211yesmaximal, characteristic, complemented
3C22×#950C211yesmaximal, characteristic, complemented
4C2×#5550C211yesmaximal, characteristic, complemented
5C2×#5239C211yesmaximal, characteristic, complemented
6C2×#5238C211yesmaximal, characteristic, complemented
7#83577C2116yesmaximal, direct product factor
8C2×#5072C211yesmaximal, characteristic, complemented
9C2×#5074C211yesmaximal, characteristic, complemented
10C2×#5037C211yesmaximal, characteristic, complemented
11C2×#5036C211yesmaximal, characteristic, complemented
12C2×#5042C211yesmaximal, characteristic, complemented
13C2×#5038C211yesmaximal, characteristic, complemented
14C2×#5028C211yesmaximal, characteristic, complemented
15C2×#5026C211yesmaximal, characteristic, complemented
16C2×#5011C211yesmaximal, characteristic, complemented
17C2×#3268—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×C3×#41C2211yescharacteristic, complemented
20C22×#235C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C3×#550—24no—
23C3×#550C2218yescomplemented
24C2×C3×#127—21no—
25C2×C3×#127C2211yescharacteristic, complemented
26C2×C3×#121—21no—
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic, complemented
30C2×C3×C4×Q8C2211yescharacteristic, complemented
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4C2211yescharacteristic
33C2×#950—28no—
34C2×#950C2218yescomplemented
35C2×#949—28no—
36C2×#949C2218yescomplemented
37C22×#216C2211yescharacteristic, complemented
38C22×#215C2211yescharacteristic
39C22×#215C2211yescharacteristic
40C2×#937—21no—
41C22×#214C2211yescharacteristic, complemented
42C22×#214C2211yescharacteristic, complemented
43C22×#213C2211yescharacteristic
44C22×#213C2211yescharacteristic
45C22×#213C2211yescharacteristic
46C22×#213C2211yescharacteristic
47C2×#930C2211yescharacteristic
48C2×#924C2211yescharacteristic
49C22×#208C2211yescharacteristic
50C23×C3⋊C8C2211yescharacteristic, complemented
51#5550—24no—
52#5550C2218yescomplemented
53C2×#894—21no—
54C2×#884—21no—
55C2×D3×C22⋊C4—21no—
56C2×#875C2211yescharacteristic
57C2×C4×D12C2211yescharacteristic
58#5239C2218yescomplemented
59#5238C2218yescomplemented
60C2×#835C2211yescharacteristic, complemented
61C2×#832C2211yescharacteristic, complemented
62C2×#832C2211yescharacteristic, complemented
63C2×#830C2211yescharacteristic
64C2×#830C2211yescharacteristic, complemented
65#5074C2218yescomplemented
66#5072C2218yescomplemented
67#5042C2218yescomplemented
68#5038C2218yescomplemented
69#5037C2218yescomplemented
70#5036C2218yescomplemented
71#5028C2218yescomplemented
72#5026C2218yescomplemented
73#5011C2218yescomplemented
74C2×#810C2211yescharacteristic, complemented
75C2×#809C2211yescharacteristic
76C2×#809C2211yescharacteristic
77C2×#807C2211yescharacteristic, complemented
78C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
79C2×#803C2211yescharacteristic, complemented
80C22×AGL(1,ℤ/8)—31no—
81C22×#135—31no—
82C2×#550D311yescharacteristic, complemented
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×#449—31no—
93C2×#447—31no—
94C2×#440—31no—
95C2×#435—31no—
96C24×D3—21no—
97C2×C3×#41—22no—
98C2×C3×#41—22no—
99C2×C3×#41—24no—
100C2×C3×#41—24no—
101C2×C3×#41—42no—
102C2×C3×#41—42no—
103C2×C3×#41C2314yes—
104C2×C3×#41C2314yescomplemented
105C22×C3×Q8C2311yescharacteristic
106C22×C3×D4—21no—
107C22×C3×D4—21no—
108C22×C3×D4—21no—
109C22×C3×D4—21no—
110C22×C3×D4—21no—
111C22×C3×D4—21no—
112C22×C3×D4D411yescharacteristic
113C22×C3×D4C2311yescharacteristic
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C23×C3×C4—21no—
117C23×C3×C4C2311yescharacteristic
118C23×C3×C4C2311yescharacteristic
119C22×#67—21no—
120C22×#67—21no—
121C2×#235—22no—
122C2×#235—24no—
123C2×#235—42no—
124C2×#235C2314yes—
125C22×D12—24no—
126C22×D12—21no—
127C22×D12—22no—
128C22×D12—42no—
129C22×D12C2311yescharacteristic
130C22×D12C2314yes—
131C22×D12C2311yescharacteristic
132C22×C4×D3—21no—
133C22×C4×D3—21no—
134C22×Dic6C2311yescharacteristic
135C3×#127—28no—
136C3×#127—22no—
137C3×#127C2314yescomplemented
138C3×#121—22no—
139C3×#121—22no—
140C3×#121—28no—
141C3×#121—28no—
142C3×#121C2314yes—
143C3×#121C2314yescomplemented
144C3×C4×Q8—22no—
145C3×C4×Q8C2314yescomplemented
146C3×C4×D4—28no—
147C3×C4×D4D414yes—
148C3×C4×D4C2314yes—
149C2×C3×C4⋊C4—21no—
150C2×C3×C4⋊C4D411yescharacteristic
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4D411yescharacteristic
155C2×C3×C22⋊C4D411yescharacteristic
156C2×C3×C42—21no—
157C2×C3×C42C2311yescharacteristic
158C2×#217—21no—
159#950—232no—
160#949—232no—
161C2×#216—24no—
162C2×#216C2314yescomplemented
163C2×#215—24no—
164C2×#215D418yescomplemented
165C2×#215C2314yes—
166C2×#215C2314yes—
167#937—28no—
168C2×#214—24no—
169C2×#214—42no—
170C2×#214C2314yescomplemented
171C2×#214C2314yescomplemented
172C2×#213—24no—
173C2×#213—24no—
174C2×#213—24no—
175C2×#213—42no—
176C2×#213C2314yes—
177C2×#213C2314yes—
178C2×#213C2314yes—
179C2×#213C2314yes—
180#930—22no—
181#930C2314yes—
182C2×(C2×D3)⋊C4—21no—
183C2×(C2×D3)⋊C4—21no—
184C2×(C2×D3)⋊C4—21no—
185C2×(C2×D3)⋊C4—21no—
186C2×C4⋊Dic3C2311yescharacteristic
187#924—22no—
188#924C2314yes—
189C2×Dic3⋊C4—21no—
190C2×#208—24no—
191C2×#208C2314yes—
192C22×C3⋊C8—24no—
193C22×C3⋊C8C2311yescharacteristic
194C22×C3⋊C8C2311yescharacteristic
195C22×C3⋊C8C2311yescharacteristic
196C22×C3⋊C8C2311yescharacteristic
197C22×C3⋊C8C2314yescomplemented
198#894—28no—
199#884—28no—
200D3×C22⋊C4—28no—
201#875—22no—
202#875C2314yes—
203C4×D12—22no—
204C4×D12C2314yes—
205#835C2314yescomplemented
206#832C2314yescomplemented
207#832C2314yescomplemented
208#830C2314yes—
209#830C2314yescomplemented
210#810C2314yescomplemented
211#809C2314yes—
212#809C2314yes—
213#807C2314yescomplemented
214C4⋊(C3⋊C8)C2314yescomplemented
215#803C2314yescomplemented
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic
218C22×#41C2×D311yescharacteristic, complemented
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×SD16—31no—
229C22×D8—31no—
230C22×D8—31no—
231C22×D8—31no—
232C22×D8—31no—
233C22×M16—31no—
234C23×C8—31no—
235#550—24no—
236#550C2×D318yescomplemented
237#546—38no—
238#546—64no—
239C2×#127—21no—
240C2×#127C2×D311yescharacteristic, complemented
241C2×#124—31no—
242C2×#123—61no—
243C2×C22⋊Q8—31no—
244C2×#121—21no—
245C2×#121—21no—
246C2×#121—31no—
247C2×#121—61no—
248C2×#121C2×D311yescharacteristic
249C2×#121C2×D311yescharacteristic, complemented
250C2×#120—61no—
251C2×C4×Q8C2×D311yescharacteristic, complemented
252C2×C4×D4—21no—
253C2×C4×D4—31no—
254C2×C4×D4C2×D311yescharacteristic
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#449—38no—
264#447—38no—
265#440—38no—
266#435—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#102—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×#97—31no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3C2×D411yescharacteristic
281C24×C3C2×D411yescharacteristic
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—24no—
285C23×D3—44no—
286C23×D3—44no—
287C23×D3—82no—
288C3×#41—28no—
289C3×#41—28no—
290C3×#41—44no—
291C3×#41—44no—
292C3×#41—48no—
293C3×#41—48no—
294C2×C3×Q8—21no—
295C2×C3×Q8—22no—
296C2×C3×Q8C2×D414yes—
297C2×C3×Q8C2412yes—
298C2×C3×D4—24no—
299C2×C3×D4—24no—
300C2×C3×D4—24no—
301C2×C3×D4—24no—
302C2×C3×D4—22no—
303C2×C3×D4—22no—
304C2×C3×D4—24no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—24no—
308C2×C3×D4—22no—
309C2×C3×D4—22no—
310C2×C3×D4—42no—
311C2×C3×D4—44no—
312C2×C3×D4—44no—
313C2×C3×D4—44no—
314C2×C3×D4—82no—
315C2×C3×D4—82no—
316C2×C3×D4—82no—
317C2×C3×D4C2×D414yes—
318C2×C3×D4C2412yes—
319C2×C3×D4C2412yes—
320C22×C3×C4—21no—
321C22×C3×C4—22no—
322C22×C3×C4—22no—
323C22×C3×C4—22no—
324C22×C3×C4—22no—
325C22×C3×C4—21no—
326C22×C3×C4—24no—
327C22×C3×C4—24no—
328C22×C3×C4—44no—
329C22×C3×C4—44no—
330C22×C3×C4C2×D411yescharacteristic
331C22×C3×C4C2×D412yes—
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2×D411yescharacteristic
334C22×C3×C4C2×D411yescharacteristic
335C22×C3×C4C2×D412yes—
336C22×C3×C4C2412yes—
337C22×C3×C4C2412yes—
338C22×C3×C4C2411yescharacteristic
339C2×#67—24no—
340C2×#67—24no—
341C2×#67—44no—
342C2×#67—82no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345#235—28no—
346#235—44no—
347#235—48no—
348C2×D12—21no—
349C2×D12—22no—
350C2×D12—22no—
351C2×D12—22no—
352C2×D12—28no—
353C2×D12—21no—
354C2×D12—24no—
355C2×D12—44no—
356C2×D12—48no—
357C2×D12—44no—
358C2×D12C2×D414yes—
359C2×D12C2412yes—
360C2×D12C2412yes—
361C2×C4×D3—24no—
362C2×C4×D3—24no—
363C2×C4×D3—44no—
364C2×C4×D3—82no—
365C2×Dic6—22no—
366C2×Dic6—22no—
367C2×Dic6—21no—
368C2×Dic6C2412yes—
369C3×C4⋊C4—24no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4C2×D414yes—
372C3×C4⋊C4C2412yes—
373C3×C22⋊C4—24no—
374C3×C22⋊C4—24no—
375C3×C22⋊C4C2×D414yes—
376C3×C22⋊C4C2×D414yes—
377C3×C42—24no—
378C3×C42C2×D412yes—
379C3×C42C2412yes—
380#217—24no—
381#216—28no—
382#215—28no—
383#215C2×D4116yescomplemented
384#214—28no—
385#214—44no—
386#213—28no—
387#213—28no—
388#213—28no—
389#213—44no—
390(C2×D3)⋊C4—24no—
391(C2×D3)⋊C4—24no—
392(C2×D3)⋊C4—24no—
393(C2×D3)⋊C4—24no—
394C4⋊Dic3—21no—
395C4⋊Dic3C2412yes—
396Dic3⋊C4—24no—
397#208—28no—
398C2×C3⋊C8—22no—
399C2×C3⋊C8—22no—
400C2×C3⋊C8—22no—
401C2×C3⋊C8—28no—
402C2×C3⋊C8C2×D414yes—
403C2×C3⋊C8C2412yes—
404C2×C3⋊C8C2412yes—
405C2×C3⋊C8C2412yes—
406C2×C3⋊C8C2412yes—
407C25—61no—
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—24no—
411C2×#41—24no—
412C2×#41—34no—
413C2×#41—42no—
414C2×#41—42no—
415C2×#41—64no—
416C2×#41—62no—
417C2×#41—122no—
418C2×#41C22×D314yes—
419C2×#41C22×D314yescomplemented
420C22×Q8—31no—
421C22×Q8C22×D311yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—31no—
429C22×D4—31no—
430C22×D4—34no—
431C22×D4—64no—
432C22×D4—61no—
433C22×D4—61no—
434C22×D4—61no—
435C22×D4—62no—
436C22×D4—122no—
437C22×D4#6711yescharacteristic
438C22×D4C22×D311yescharacteristic
439C22×D4C22×D311yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—61no—
443C23×C4—61no—
444C23×C4C22×D311yescharacteristic
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—34no—
455C2×SD16—64no—
456C2×SD16—64no—
457C2×SD16—122no—
458C2×D8—34no—
459C2×D8—34no—
460C2×D8—34no—
461C2×D8—34no—
462C2×D8—64no—
463C2×D8—64no—
464C2×D8—64no—
465C2×D8—122no—
466C2×M16—34no—
467C2×M16—64no—
468C22×C8—31no—
469C22×C8—31no—
470C22×C8—34no—
471C22×C8—31no—
472C22×C8—31no—
473C22×C8—64no—
474#127—28no—
475#127—22no—
476#127C22×D314yescomplemented
477#124—34no—
478#124—62no—
479#123—68no—
480C22⋊Q8—34no—
481C22⋊Q8—62no—
482#121—22no—
483#121—22no—
484#121—28no—
485#121—28no—
486#121—34no—
487#121—62no—
488#121—68no—
489#121C22×D314yes—
490#121C22×D314yescomplemented
491#120—68no—
492C4×Q8—22no—
493C4×Q8C22×D314yescomplemented
494C4×D4—28no—
495C4×D4—34no—
496C4×D4—62no—
497C4×D4#6714yes—
498C4×D4C22×D314yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—61no—
502C2×C4⋊C4#6711yescharacteristic
503C2×C4⋊C4C22×D311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—68no—
512C2×C22⋊C4#6711yescharacteristic
513C2×C22⋊C4#6711yescharacteristic
514C2×C42—21no—
515C2×C42C22×D311yescharacteristic
516#107—34no—
517C4⋊C8—34no—
518#103—34no—
519#103—34no—
520#102—34no—
521#102—34no—
522#102—34no—
523#102—34no—
524C22⋊C8—34no—
525C22⋊C8—34no—
526#97—34no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—42no—
536C23×C3—42no—
537C23×C3—42no—
538C23×C3—42no—
539C23×C3—42no—
540C23×C3—42no—
541C23×C3C22×D412yes—
542C23×C3C22×D412yes—
543C23×C3C22×D411yescharacteristic
544C22×D3—24no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—48no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—48no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—84no—
555C22×D3—816no—
556C3×Q8—24no—
557C3×Q8—22no—
558C3×Q8C22×D414yes—
559C3×D4—22no—
560C3×D4—22no—
561C3×D4—22no—
562C3×D4—22no—
563C3×D4—44no—
564C3×D4—48no—
565C3×D4—48no—
566C3×D4—48no—
567C3×D4—42no—
568C3×D4—42no—
569C3×D4—84no—
570C3×D4—84no—
571C3×D4—84no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—24no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—24no—
579C2×C3×C4—24no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—48no—
586C2×C3×C4—48no—
587C2×C3×C4—42no—
588C2×C3×C4C22×D412yes—
589C2×C3×C4C22×D412yes—
590C2×C3×C4C22×D412yes—
591C2×C3×C4C22×D412yes—
592C2×C3×C4C22×D412yes—
593C2×C3×C4C22×D411yescharacteristic
594C2×C3×C4H(5,𝔽2)12yes—
595C2×C3×C4C2511yescharacteristic
596#67—48no—
597#67—84no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—42no—
601C2×Dic3—42no—
602D12—24no—
603D12—22no—
604D12—22no—
605D12—22no—
606D12—48no—
607D12—42no—
608D12C22×D414yes—
609C4×D3—48no—
610C4×D3—84no—
611Dic6—22no—
612Dic6—22no—
613Dic6—42no—
614C3⋊C8—22no—
615C3⋊C8—22no—
616C3⋊C8—22no—
617C3⋊C8C22×D414yes—
618C24—21no—
619C24—21no—
620C24—61no—
621C24—61no—
622C24—64no—
623C24—124no—
624C24—124no—
625C24—242no—
626C24C2×#6711yescharacteristic
627C24C2×#6711yescharacteristic
628#41—28no—
629#41—28no—
630#41—44no—
631#41—44no—
632#41—48no—
633#41—48no—
634#41—68no—
635#41—124no—
636#41—128no—
637C2×Q8—22no—
638C2×Q8—21no—
639C2×Q8—32no—
640C2×Q8—61no—
641C2×Q8—62no—
642C2×Q8—62no—
643C2×Q8D3×D414yes—
644C2×Q8C23×D312yes—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—24no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—24no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—24no—
657C2×D4—34no—
658C2×D4—32no—
659C2×D4—32no—
660C2×D4—42no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—68no—
665C2×D4—64no—
666C2×D4—64no—
667C2×D4—62no—
668C2×D4—62no—
669C2×D4—62no—
670C2×D4—61no—
671C2×D4—64no—
672C2×D4—61no—
673C2×D4—82no—
674C2×D4—82no—
675C2×D4—82no—
676C2×D4—124no—
677C2×D4—128no—
678C2×D4—124no—
679C2×D4—124no—
680C2×D4—242no—
681C2×D4C2×#6714yes—
682C2×D4C23×D312yes—
683C2×D4C23×D312yes—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—64no—
697C22×C4—64no—
698C22×C4—124no—
699C22×C4—242no—
700C22×C4C2×#6712yes—
701C22×C4C2×#6712yes—
702C22×C4C2×#6711yescharacteristic
703C22×C4C2×#6711yescharacteristic
704C22×C4C2×#6711yescharacteristic
705C22×C4C2×#6711yescharacteristic
706C22×C4C23×D312yes—
707C22×C4C23×D312yes—
708C22×C4C23×D311yescharacteristic
709Q16—68no—
710SD16—316no—
711SD16—68no—
712SD16—68no—
713SD16—124no—
714D8—68no—
715D8—68no—
716D8—68no—
717D8—124no—
718M16—68no—
719C2×C8—34no—
720C2×C8—32no—
721C2×C8—32no—
722C2×C8—32no—
723C2×C8—32no—
724C2×C8—68no—
725C2×C8—62no—
726C2×C8—62no—
727C2×C8—62no—
728C4⋊C4—24no—
729C4⋊C4—21no—
730C4⋊C4—32no—
731C4⋊C4—61no—
732C4⋊C4—64no—
733C4⋊C4C2×#6714yes—
734C4⋊C4C23×D312yes—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—64no—
738C22⋊C4—64no—
739C22⋊C4—64no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C22⋊C4C2×#6714yes—
743C22⋊C4C2×#6714yes—
744C42—24no—
745C42C2×#6712yes—
746C42C23×D312yes—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—44no—
754C22×C3—44no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—84no—
762C22×C3—84no—
763C22×C3D4212yes—
764C22×C3#57512yes—
765C22×C3#57612yes—
766C22×C3C23×D411yescharacteristic
767C2×D3—24no—
768C2×D3—48no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C2×D3—42no—
774C2×D3—816no—
775C2×D3—84no—
776C3×C4—22no—
777C3×C4—22no—
778C3×C4—24no—
779C3×C4—22no—
780C3×C4—22no—
781C3×C4—42no—
782C3×C4D4212yes—
783C3×C4C23×D411yescharacteristic
784C3×C4C2×H(5,𝔽2)11yescharacteristic
785Dic3—42no—
786Dic3—42no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—62no—
802C23—64no—
803C23—62no—
804C23—128no—
805C23—128no—
806C23—122no—
807C23—122no—
808C23—122no—
809C23—122no—
810C23—122no—
811C23—244no—
812C23—2416no—
813C23C22×#6712yes—
814C23C22×#6712yes—
815C23C22×#6711yescharacteristic
816Q8—22no—
817Q8—24no—
818Q8—62no—
819Q8—62no—
820Q8—122no—
821Q8C2×D3×D414yes—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—34no—
827D4—44no—
828D4—48no—
829D4—48no—
830D4—48no—
831D4—42no—
832D4—42no—
833D4—62no—
834D4—62no—
835D4—62no—
836D4—64no—
837D4—84no—
838D4—84no—
839D4—84no—
840D4—128no—
841D4—128no—
842D4—122no—
843D4—244no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—48no—
858C2×C4—48no—
859C2×C4—42no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—128no—
863C2×C4—122no—
864C2×C4—122no—
865C2×C4—244no—
866C2×C4C2×D3×D412yes—
867C2×C4#100412yes—
868C2×C4C22×#6712yes—
869C2×C4C22×#6712yes—
870C2×C4C22×#6712yes—
871C2×C4C22×#6712yes—
872C2×C4C22×#6711yescharacteristic
873C2×C4C24×D311yescharacteristic
874C8—34no—
875C8—62no—
876C8—62no—
877C8—62no—
878C2×C3—42no—
879C2×C3—42no—
880C2×C3—82no—
881C2×C3—82no—
882C2×C3#326814yescomplemented
883C2×C3C2×D4211yescharacteristic
884C2×C3C2×#57511yescharacteristic
885C2×C3C2×#57611yescharacteristic
886D3—44no—
887D3—82no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—44no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—64no—
903C22—84no—
904C22—84no—
905C22—128no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—2416no—
912C22—244no—
913C22D4×#6712yes—
914C22#582212yes—
915C22#583512yes—
916C22C23×#6711yescharacteristic
917C4—22no—
918C4—22no—
919C4—24no—
920C4—22no—
921C4—22no—
922C4—42no—
923C4—122no—
924C4—122no—
925C4D4×#6712yes—
926C4C22×D3×D411yescharacteristic
927C4C2×#100411yescharacteristic
928C3C2×#326811yescharacteristic, complemented, Sylow
929C2—42no—
930C2—42no—
931C2—82no—
932C2—82no—
933C2—124no—
934C2—242no—
935C2#8357714yesdirect product factor
936C2C2×D4×#6711yescharacteristic
937C2C2×#582211yescharacteristic
938C2C2×#583511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#550C2
socleC23×C3C22×D4
hypercenterC2×#550D3
hypocenterC3C2×#3268
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×C3×#550C2semidirect
2. C22×#949C2semidirect
3. C22×#950C2semidirect
4. C2×#5550C2semidirect
5. C2×#5239C2semidirect
6. C2×#5238C2semidirect
7. #83577C2direct (N × H)
8. C2×#5072C2semidirect
9. C2×#5074C2semidirect
10. C2×#5037C2semidirect
11. C2×#5036C2semidirect
12. C2×#5042C2semidirect
13. C2×#5038C2semidirect
14. C2×#5028C2semidirect
15. C2×#5026C2semidirect
16. C2×#5011C2semidirect
19. C22×C3×#41C22semidirect
23. C3×#550C22semidirect
25. C2×C3×#127C22semidirect
29. C2×C3×#121C22semidirect
30. C2×C3×C4×Q8C22semidirect
34. C2×#950C22semidirect
36. C2×#949C22semidirect
37. C22×#216C22semidirect
41. C22×#214C22semidirect
42. C22×#214C22semidirect
50. C23×C3⋊C8C22semidirect
52. #5550C22semidirect
58. #5239C22semidirect
59. #5238C22semidirect
60. C2×#835C22semidirect
61. C2×#832C22semidirect
62. C2×#832C22semidirect
64. C2×#830C22semidirect
65. #5074C22semidirect
66. #5072C22semidirect
67. #5042C22semidirect
68. #5038C22semidirect
69. #5037C22semidirect
70. #5036C22semidirect
71. #5028C22semidirect
72. #5026C22semidirect
73. #5011C22semidirect
74. C2×#810C22semidirect
77. C2×#807C22semidirect
78. C2×C4⋊(C3⋊C8)C22semidirect
79. C2×#803C22semidirect
82. C2×#550D3semidirect
104. C2×C3×#41C23semidirect
137. C3×#127C23semidirect
143. C3×#121C23semidirect
145. C3×C4×Q8C23semidirect
162. C2×#216C23semidirect
164. C2×#215D4semidirect
170. C2×#214C23semidirect
171. C2×#214C23semidirect
197. C22×C3⋊C8C23semidirect
205. #835C23semidirect
206. #832C23semidirect
207. #832C23semidirect
209. #830C23semidirect
210. #810C23semidirect
213. #807C23semidirect
214. C4⋊(C3⋊C8)C23semidirect
215. #803C23semidirect
218. C22×#41C2×D3semidirect
236. #550C2×D3semidirect
240. C2×#127C2×D3semidirect
249. C2×#121C2×D3semidirect
251. C2×C4×Q8C2×D3semidirect
383. #215C2×D4semidirect
419. C2×#41C22×D3semidirect
476. #127C22×D3semidirect
490. #121C22×D3semidirect
493. C4×Q8C22×D3semidirect
882. C2×C3#3268semidirect
928. C3C2×#3268semidirect
935. C2#83577direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5502
C22×#9492
C22×#9502
C2×#55502
C2×#52392
C2×#52382
#835772
C2×#50722
C2×#50742
C2×#50372
C2×#50362
C2×#50422
C2×#50382
C2×#50282
C2×#50262
C2×#50112
C2×#32683