Finite Group Databasebeta

← C2×#83061 #10964636

Subgroups — C2×#83061 #10964636

Order 768.

3158 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#125C211yesmaximal, characteristic, complemented
2C22×#895C211yesmaximal, characteristic
3#83061C2116yesmaximal, direct product factor
4C2×#4992C212yesmaximal, complemented
5C2×#4991C212yesmaximal, complemented
6C2×#4987C211yesmaximal, characteristic, complemented
7C2×#4988C211yesmaximal, characteristic, complemented
8C2×#4988C212yesmaximal, complemented
9C2×#4990C212yesmaximal, complemented
10C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
11C2×#4939C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13C2×#2490—31nomaximal, Sylow
14C23×D12C2211yescharacteristic
15C23×D12C2212yes—
16C23×C4×D3C2211yescharacteristic
17C2×C3×#125—28no—
18C2×C3×#125C2218yescomplemented
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C4⋊C4C2212yes—
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×(C2×D3)⋊C4C2212yes—
30C22×(C2×D3)⋊C4C2212yes—
31C22×(C2×D3)⋊C4C2212yes—
32C22×C4⋊Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C22×C4×Dic3C2212yes—
35C2×#895—28no—
36C2×#895C2218yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41#4992C22116yescomplemented
42#4991C22116yescomplemented
43#4990C22116yescomplemented
44#4988C2218yescomplemented
45#4988C22116yescomplemented
46#4987C2218yescomplemented
47Dic3×C4⋊C4C2218yescomplemented
48#4939C2218yescomplemented
49C4×(C2×D3)⋊C4C2218yescomplemented
50C22×#125D311yescharacteristic, complemented
51C22×#121—31no—
52#2490—316no—
53C2×#397—32no—
54C2×#394—32no—
55C2×#390—31no—
56C2×#390—32no—
57C2×#390—31no—
58C2×#388—32no—
59C2×#380—31no—
60C2×C4×C4⋊C4—31no—
61C2×C4×C22⋊C4—31no—
62C24×D3C2312yes—
63C24×D3C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2312yes—
67C23×C3×C4C2312yes—
68C23×C3×C4C2311yescharacteristic
69C23×Dic3C2311yescharacteristic
70C23×Dic3C2311yescharacteristic
71C23×Dic3C2312yes—
72C23×Dic3C2311yescharacteristic
73C22×D12—28no—
74C22×D12—28no—
75C22×D12—24no—
76C22×D12—24no—
77C22×D12—24no—
78C22×D12—44no—
79C22×D12C2314yes—
80C22×D12C2318yes—
81C22×C4×D3—24no—
82C22×C4×D3—24no—
83C22×C4×D3—24no—
84C22×C4×D3C2314yes—
85C3×#125—232no—
86C2×C3×C4⋊C4—28no—
87C2×C3×C4⋊C4—28no—
88C2×C3×C4⋊C4—24no—
89C2×C3×C4⋊C4D418yes—
90C2×C3×C4⋊C4C2314yes—
91C2×C3×C4⋊C4C2318yes—
92C2×C3×C4⋊C4C2318yes—
93C2×C3×C4⋊C4C2314yes—
94C2×C3×C42—24no—
95C2×C3×C42C2314yes—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—28no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—28no—
100C2×(C2×D3)⋊C4—44no—
101C2×(C2×D3)⋊C4—44no—
102C2×(C2×D3)⋊C4—44no—
103C2×(C2×D3)⋊C4—44no—
104C2×(C2×D3)⋊C4C2314yes—
105C2×(C2×D3)⋊C4C2314yes—
106C2×(C2×D3)⋊C4C2318yes—
107C2×(C2×D3)⋊C4C2318yes—
108C2×(C2×D3)⋊C4C2318yes—
109C2×(C2×D3)⋊C4C2318yes—
110C2×(C2×D3)⋊C4C2318yes—
111C2×(C2×D3)⋊C4C2318yes—
112C2×C4⋊Dic3—24no—
113C2×C4⋊Dic3C2314yes—
114C2×C4×Dic3—24no—
115C2×C4×Dic3—44no—
116C2×C4×Dic3C2314yes—
117C2×C4×Dic3C2318yes—
118#895—232no—
119C3⋊#95C2314yes—
120C3⋊#95C2314yes—
121C3⋊#95C2318yes—
122C3⋊#95C2318yes—
123C23×D4—31no—
124C23×D4—32no—
125C24×C4—31no—
126C2×#125—28no—
127C2×#125C2×D318yescomplemented
128C2×#121—38no—
129C2×#121—68no—
130C22×C4⋊C4—31no—
131C22×C4⋊C4C2×D312yes—
132C22×C4⋊C4C2×D312yes—
133C22×C4⋊C4C2×D311yescharacteristic
134C22×C4⋊C4C2×D311yescharacteristic
135C22×C22⋊C4—31no—
136C22×C22⋊C4—32no—
137C22×C22⋊C4—31no—
138C22×C22⋊C4—32no—
139C22×C22⋊C4—32no—
140C22×C22⋊C4—32no—
141C22×C22⋊C4—32no—
142C22×C22⋊C4—32no—
143C22×C42—31no—
144C22×C42—32no—
145C22×C42C2×D311yescharacteristic
146#397—316no—
147#394—316no—
148#390—38no—
149#390—316no—
150#390—38no—
151#388—316no—
152#380—38no—
153C4×C4⋊C4—38no—
154C4×C22⋊C4—38no—
155C2×#95—32no—
156C2×#95—31no—
157C2×#95—32no—
158C2×#95—31no—
159C24×C3C2411yescharacteristic
160C23×D3—22no—
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—24no—
167C23×D3—24no—
168C23×D3—24no—
169C23×D3—24no—
170C23×D3—24no—
171C23×D3—24no—
172C23×D3—24no—
173C23×D3#4114yes—
174C23×D3C2414yes—
175C23×D3C2412yes—
176C22×C3×C4—24no—
177C22×C3×C4—24no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—24no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—24no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—24no—
187C22×C3×C4C2×D418yes—
188C22×C3×C4C2×D414yes—
189C22×C3×C4#4114yes—
190C22×C3×C4#4114yes—
191C22×C3×C4C2412yes—
192C22×C3×C4C2412yes—
193C22×C3×C4C2414yes—
194C22×C3×C4C2414yes—
195C22×C3×C4C2412yes—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—24no—
201C22×Dic3—22no—
202C22×Dic3—22no—
203C22×Dic3—22no—
204C22×Dic3—24no—
205C22×Dic3—24no—
206C22×Dic3—22no—
207C22×Dic3#4114yes—
208C22×Dic3C2412yes—
209C22×Dic3C2412yes—
210C22×Dic3C2414yes—
211C22×Dic3C2412yes—
212C2×D12—216no—
213C2×D12—216no—
214C2×D12—28no—
215C2×D12—28no—
216C2×D12—28no—
217C2×D12—48no—
218C2×D12—432no—
219C2×D12—416no—
220C2×C4×D3—28no—
221C2×C4×D3—28no—
222C2×C4×D3—28no—
223C2×C4×D3—416no—
224C3×C4⋊C4—216no—
225C3×C4⋊C4—216no—
226C3×C4⋊C4—28no—
227C3×C4⋊C4C2×D4116yes—
228C3×C42—28no—
229(C2×D3)⋊C4—28no—
230(C2×D3)⋊C4—216no—
231(C2×D3)⋊C4—28no—
232(C2×D3)⋊C4—216no—
233(C2×D3)⋊C4—48no—
234(C2×D3)⋊C4—48no—
235(C2×D3)⋊C4—48no—
236(C2×D3)⋊C4—48no—
237C4⋊Dic3—28no—
238C4×Dic3—28no—
239C4×Dic3—48no—
240C25—31no—
241C25—32no—
242C22×D4—34no—
243C22×D4—38no—
244C22×D4—68no—
245C22×D4—64no—
246C22×D4—64no—
247C22×D4—68no—
248C22×D4—64no—
249C22×D4—124no—
250C23×C4—31no—
251C23×C4—32no—
252C23×C4—31no—
253C23×C4—31no—
254C23×C4—34no—
255C23×C4—64no—
256C23×C4—64no—
257C23×C4—64no—
258C23×C4C22×D312yes—
259C23×C4C22×D311yescharacteristic
260C23×C4C22×D311yescharacteristic
261C23×C4C22×D312yes—
262C23×C4C22×D311yescharacteristic
263#125—232no—
264#121—632no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—34no—
269C2×C4⋊C4—64no—
270C2×C4⋊C4#6718yes—
271C2×C4⋊C4C22×D314yes—
272C2×C4⋊C4C22×D318yes—
273C2×C4⋊C4C22×D318yes—
274C2×C4⋊C4C22×D314yes—
275C2×C22⋊C4—38no—
276C2×C22⋊C4—34no—
277C2×C22⋊C4—34no—
278C2×C22⋊C4—38no—
279C2×C22⋊C4—38no—
280C2×C22⋊C4—38no—
281C2×C22⋊C4—38no—
282C2×C22⋊C4—38no—
283C2×C22⋊C4—64no—
284C2×C22⋊C4—68no—
285C2×C22⋊C4—64no—
286C2×C22⋊C4—68no—
287C2×C22⋊C4—124no—
288C2×C22⋊C4—124no—
289C2×C22⋊C4—124no—
290C2×C22⋊C4—124no—
291C2×C42—24no—
292C2×C42—34no—
293C2×C42—38no—
294C2×C42—64no—
295C2×C42—124no—
296C2×C42C22×D314yes—
297#95—34no—
298#95—34no—
299#95—38no—
300#95—38no—
301C23×C3C22×D412yes—
302C23×C3C2×#4112yes—
303C23×C3C2×#4112yes—
304C23×C3C2×#4112yes—
305C23×C3C2×#4112yes—
306C23×C3H(5,𝔽2)12yes—
307C23×C3H(5,𝔽2)12yes—
308C23×C3C2511yescharacteristic
309C22×D3—28no—
310C22×D3—28no—
311C22×D3—28no—
312C22×D3—22no—
313C22×D3—22no—
314C22×D3—22no—
315C22×D3—22no—
316C22×D3—22no—
317C22×D3—22no—
318C22×D3—24no—
319C22×D3—24no—
320C22×D3—24no—
321C22×D3—24no—
322C22×D3—24no—
323C22×D3—24no—
324C22×D3—24no—
325C22×D3—44no—
326C22×D3—44no—
327C22×D3—44no—
328C22×D3—44no—
329C22×D3—48no—
330C22×D3—48no—
331C22×D3—48no—
332C22×D3—48no—
333C22×D3—48no—
334C22×D3—48no—
335C22×D3—48no—
336C22×D3C2×#4114yes—
337C2×C3×C4—216no—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—24no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—24no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—24no—
349C2×C3×C4—44no—
350C2×C3×C4—44no—
351C2×C3×C4—48no—
352C2×C3×C4#124116yes—
353C2×C3×C4C22×D418yes—
354C2×C3×C4C22×D414yes—
355C2×C3×C4C2×#4114yes—
356C2×C3×C4C2×#4114yes—
357C2×Dic3—28no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—24no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—24no—
367C2×Dic3—24no—
368C2×Dic3—22no—
369C2×Dic3—44no—
370C2×Dic3—48no—
371C2×Dic3—44no—
372C2×Dic3C2×#4114yes—
373D12—432no—
374D12—416no—
375C4×D3—416no—
376C24—34no—
377C24—32no—
378C24—34no—
379C24—62no—
380C24—62no—
381C24—62no—
382C24—62no—
383C24—62no—
384C24—62no—
385C24—64no—
386C24—64no—
387C24—64no—
388C24—64no—
389C24—64no—
390C24—64no—
391C24—64no—
392C24C23×D311yescharacteristic
393C2×D4—616no—
394C2×D4—68no—
395C2×D4—68no—
396C2×D4—616no—
397C2×D4—68no—
398C2×D4—128no—
399C2×D4—1232no—
400C2×D4—1216no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—34no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—34no—
417C22×C4—62no—
418C22×C4—62no—
419C22×C4—62no—
420C22×C4—64no—
421C22×C4—62no—
422C22×C4—62no—
423C22×C4—62no—
424C22×C4—64no—
425C22×C4—62no—
426C22×C4—64no—
427C22×C4—62no—
428C22×C4—68no—
429C22×C4—68no—
430C22×C4—68no—
431C22×C4—1216no—
432C22×C4#23914yes—
433C22×C4#23914yes—
434C22×C4C2×#6718yes—
435C22×C4C2×#6714yes—
436C22×C4C23×D312yes—
437C22×C4C23×D312yes—
438C22×C4C23×D314yes—
439C22×C4C23×D314yes—
440C22×C4C23×D312yes—
441C4⋊C4—216no—
442C4⋊C4—216no—
443C4⋊C4—28no—
444C4⋊C4—68no—
445C4⋊C4C2×#67116yes—
446C22⋊C4—68no—
447C22⋊C4—616no—
448C22⋊C4—68no—
449C22⋊C4—616no—
450C22⋊C4—128no—
451C22⋊C4—128no—
452C22⋊C4—128no—
453C22⋊C4—128no—
454C42—28no—
455C42—68no—
456C42—128no—
457C22×C3C2×#12414yes—
458C22×C3#52914yes—
459C22×C3#54014yes—
460C22×C3#54614yes—
461C22×C3#55014yes—
462C22×C3#55314yes—
463C22×C3#55314yes—
464C22×C3C23×D411yescharacteristic
465C22×C3C22×#4111yescharacteristic
466C22×C3C22×#4111yescharacteristic
467C22×C3C22×#4111yescharacteristic
468C22×C3C22×#4111yescharacteristic
469C22×C3C2×H(5,𝔽2)11yescharacteristic
470C22×C3C2×H(5,𝔽2)11yescharacteristic
471C2×D3—24no—
472C2×D3—24no—
473C2×D3—24no—
474C2×D3—42no—
475C2×D3—42no—
476C2×D3—42no—
477C2×D3—42no—
478C2×D3—416no—
479C2×D3—44no—
480C2×D3—44no—
481C2×D3—44no—
482C2×D3—44no—
483C2×D3—44no—
484C2×D3—44no—
485C2×D3—44no—
486C2×D3—816no—
487C3×C4—28no—
488C3×C4—42no—
489C3×C4—42no—
490C3×C4—44no—
491C3×C4C2×#12418yes—
492Dic3—24no—
493Dic3—42no—
494Dic3—44no—
495Dic3—42no—
496C23—34no—
497C23—68no—
498C23—68no—
499C23—62no—
500C23—62no—
501C23—62no—
502C23—62no—
503C23—62no—
504C23—62no—
505C23—68no—
506C23—64no—
507C23—64no—
508C23—64no—
509C23—64no—
510C23—64no—
511C23—64no—
512C23—64no—
513C23—124no—
514C23—124no—
515C23—124no—
516C23—124no—
517C23—128no—
518C23—128no—
519C23—128no—
520C23—128no—
521C23—128no—
522C23—128no—
523C23—128no—
524C23C2×#23912yes—
525C23C2×#23912yes—
526C23D3×#4112yes—
527C23D3×#4112yes—
528C23#100912yes—
529C23#100912yes—
530C23C22×#6712yes—
531C23C24×D311yescharacteristic
532D4—1232no—
533D4—1216no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—216no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—34no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—48no—
550C2×C4—68no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—64no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—64no—
559C2×C4—64no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—124no—
563C2×C4—128no—
564C2×C4—124no—
565C2×C4—1216no—
566C2×C4#947116yes—
567C2×C4C2×#23914yes—
568C2×C4C2×#23914yes—
569C2×C4C22×#6718yes—
570C2×C4C22×#6714yes—
571C2×C3#249018yescomplemented
572C2×C3C22×#12411yescharacteristic
573C2×C3C2×#52911yescharacteristic
574C2×C3C2×#54011yescharacteristic
575C2×C3C2×#54611yescharacteristic
576C2×C3C2×#55011yescharacteristic
577C2×C3C2×#55311yescharacteristic
578C2×C3C2×#55311yescharacteristic
579D3—44no—
580D3—84no—
581C22—64no—
582C22—64no—
583C22—64no—
584C22—122no—
585C22—122no—
586C22—1216no—
587C22—122no—
588C22—122no—
589C22—124no—
590C22—124no—
591C22—124no—
592C22—124no—
593C22—124no—
594C22—124no—
595C22—124no—
596C22—2416no—
597C22#569114yes—
598C22#569514yes—
599C22#569514yes—
600C22#569714yes—
601C22C2×#94714yes—
602C22#582914yes—
603C22#583414yes—
604C22C22×#23911yescharacteristic
605C22C22×#23911yescharacteristic
606C22C2×D3×#4111yescharacteristic
607C22C2×D3×#4111yescharacteristic
608C22C2×#100911yescharacteristic
609C22C2×#100911yescharacteristic
610C22C23×#6711yescharacteristic
611C4—28no—
612C4—42no—
613C4—42no—
614C4—44no—
615C4—64no—
616C4—124no—
617C4—122no—
618C4—122no—
619C4C2×#94718yes—
620C3C2×#249011yescharacteristic, complemented, Sylow
621C2—124no—
622C2—244no—
623C2#8306118yesdirect product factor
624C2C2×#569111yescharacteristic
625C2C2×#569711yescharacteristic
626C2C2×#569511yescharacteristic
627C2C2×#569511yescharacteristic
628C2C22×#94711yescharacteristic
629C2C2×#582911yescharacteristic
630C2C2×#583411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#125C2
socleC24×C3C24
prime radicalC22×#895C2
hypercenterC22×#125D3
hypocenterC3C2×#2490
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. C22×C3×#125C2semidirect
3. #83061C2direct (N × H)
4. C2×#4992C2semidirect
5. C2×#4991C2semidirect
6. C2×#4987C2semidirect
7. C2×#4988C2semidirect
8. C2×#4988C2semidirect
9. C2×#4990C2semidirect
10. C2×Dic3×C4⋊C4C2semidirect
11. C2×#4939C2semidirect
12. C2×C4×(C2×D3)⋊C4C2semidirect
18. C2×C3×#125C22semidirect
41. #4992C22semidirect
42. #4991C22semidirect
43. #4990C22semidirect
44. #4988C22semidirect
45. #4988C22semidirect
46. #4987C22semidirect
47. Dic3×C4⋊C4C22semidirect
48. #4939C22semidirect
49. C4×(C2×D3)⋊C4C22semidirect
50. C22×#125D3semidirect
127. C2×#125C2×D3semidirect
571. C2×C3#2490semidirect
620. C3C2×#2490semidirect
623. C2#83061direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1252
C22×#8952
#830612
C2×#49922
C2×#49912
C2×#49872
C2×#49882
C2×#49902
C2×Dic3×C4⋊C42
C2×#49392
C2×C4×(C2×D3)⋊C42
C2×#24903