Finite Group Databasebeta

← #13161948

Subgroups — #13161948

Order 1728.

1208 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#3753C211yesmaximal, characteristic, complemented
3#11723696C211yesmaximal, characteristic, complemented
4C2×#88810C211yesmaximal, characteristic, complemented
5C3×#63659C211yesmaximal, characteristic, complemented
6#11722075C211yesmaximal, characteristic, complemented
7#11722072C211yesmaximal, characteristic, complemented
8#10591456—31nomaximal
9#10591448—31nomaximal
10#10591447—31nomaximal
11C23×C3×C3⋊D3—21no—
12C2×C33×D4C2211yescharacteristic
13C2×C3×#638—21no—
14C3×D4×C3⋊D3—22no—
15C3×D4×C3⋊D3—22no—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×#6295—21no—
20C3×#3753—22no—
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24#88814—21no—
25#88810—22no—
26C2×D4×C3⋊D3D311yescharacteristic, complemented
27C2×C3×D3×D4—31no—
28C2×C3×D3×D4—31no—
29C2×C3×D3×D4—61no—
30C2×#3753D311yescharacteristic, complemented
31C2×C3×#213—31no—
32C2×C3×#213—31no—
33C2×C3×#213—61no—
34#63916—31no—
35#63909—31no—
36#63908—31no—
37C2×#3714—31no—
38C2×#3714—31no—
39C2×#3713—31no—
40#63659D311yescharacteristic, complemented
41C3×#832—31no—
42C3×#832—31no—
43C3×#832—61no—
44#63564—31no—
45#63563—31no—
46#63562—31no—
47#63557—31no—
48(C2×D3)⋊(C3⋊C8)—31no—
49(C2×D3)⋊(C3⋊C8)—31no—
50C23×C33—21no—
51C22×C3×C3⋊D3—24no—
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—21no—
54C22×C3×C3⋊D3—42no—
55C22×C3×C3⋊D3—42no—
56C22×C3×C3⋊D3D411yescharacteristic
57C33×D4—21no—
58C33×D4D412yescomplemented
59C2×C33×C4C2311yescharacteristic
60C3×#638—24no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3D411yescharacteristic
63C3×C4⋊(C3⋊D3)—21no—
64C3×C4⋊(C3⋊D3)—21no—
65C3×C4⋊(C3⋊D3)—21no—
66C3×C4⋊(C3⋊D3)D412yescomplemented
67C3×C4×C3⋊D3—21no—
68C3×C4×C3⋊D3—21no—
69#6295—42no—
70C3×C3⋊(C3⋊C8)—21no—
71C3×C3⋊(C3⋊C8)—21no—
72#5217—91no—
73#5156—91no—
74#4773—91no—
75C23×C3⋊D3—21no—
76C23×C3×D3—61no—
77C23×C3×D3—61no—
78C23×C3×D3—62no—
79C2×C32×D4—21no—
80C2×C32×D4—21no—
81C2×C32×D4—21no—
82C2×C32×D4—41no—
83C2×C32×D4C2×D311yescharacteristic
84C2×C32×D4C2×D311yescharacteristic
85C2×C32×D4C2×D311yescharacteristic
86C2×#638—21no—
87D4×C3⋊D3—22no—
88D4×C3⋊D3—22no—
89C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
90C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
91C2×C4×C3⋊D3C2×D311yescharacteristic
92C2×C3×#67—61no—
93C2×C3×#67—61no—
94C2×C3×#67—62no—
95C3×D3×D4—62no—
96C3×D3×D4—62no—
97C3×D3×D4—64no—
98C3×D3×D4—64no—
99C3×D3×D4—62no—
100C3×D3×D4—62no—
101C2×C3×D12—31no—
102C2×C3×D12—31no—
103C2×C3×D12—31no—
104C2×C3×D12—31no—
105C2×C3×D12—61no—
106C2×C3×D12—61no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—61no—
110C2×#626—61no—
111C2×#626—61no—
112C2×#625—61no—
113#3753—22no—
114C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
115C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
116C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
117C3×#213—64no—
118C3×#213—62no—
119C3×#213—62no—
120C3×C4⋊Dic3—31no—
121C3×C4⋊Dic3—31no—
122C3×C4⋊Dic3—61no—
123C2×C3×C3⋊C8—31no—
124C2×C3×C3⋊C8—31no—
125C2×C3×C3⋊C8—31no—
126C2×C3×C3⋊C8—31no—
127C2×C3×C3⋊C8—61no—
128C2×C3×C3⋊C8—61no—
129#3722—61no—
130(C2×D3)⋊Dic3—61no—
131(C2×D3)⋊Dic3—61no—
132#3714—62no—
133#3714—62no—
134#3713—62no—
135C22×C33—22no—
136C22×C33—41no—
137C22×C33—41no—
138C22×C33C2×D411yescharacteristic
139C2×C3×C3⋊D3—21no—
140C2×C3×C3⋊D3—21no—
141C2×C3×C3⋊D3—22no—
142C2×C3×C3⋊D3—48no—
143C2×C3×C3⋊D3—41no—
144C2×C3×C3⋊D3—41no—
145C2×C3×C3⋊D3—41no—
146C2×C3×C3⋊D3—41no—
147C2×C3×C3⋊D3—41no—
148C2×C3×C3⋊D3D812yescomplemented
149C33×C4C2×D411yescharacteristic
150C33×C4C2×D411yescharacteristic
151C3×C3⋊Dic3—21no—
152C3×C3⋊Dic3—41no—
153C22×C3×D4—91no—
154C2×D3×D4—31no—
155C2×D3×D4—31no—
156C2×D3×D4—61no—
157C2×C3×D8—91no—
158#938—91no—
159C2×#213—31no—
160C2×#213—31no—
161C2×#213—61no—
162C2×#213—91no—
163C2×#213—91no—
164#930—91no—
165C2×D24—91no—
166#895—91no—
167C3×#102—91no—
168#832—31no—
169#832—31no—
170#832—61no—
171#832—91no—
172#830—91no—
173#821—91no—
174(C2×D3)⋊C8—91no—
175(C2×D3)⋊C8—91no—
176#809—91no—
177C23×C32—21no—
178C23×C32—22no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—41no—
182C23×C32—41no—
183C23×C32—42no—
184C22×C3⋊D3—24no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3—21no—
187C22×C3⋊D3—42no—
188C22×C3⋊D3—42no—
189C22×C3⋊D3#6711yescharacteristic
190C22×C3×D3—31no—
191C22×C3×D3—31no—
192C22×C3×D3—61no—
193C22×C3×D3—62no—
194C22×C3×D3—68no—
195C22×C3×D3—64no—
196C22×C3×D3—64no—
197C22×C3×D3—61no—
198C22×C3×D3—61no—
199C22×C3×D3—61no—
200C22×C3×D3—61no—
201C22×C3×D3—121no—
202C22×C3×D3—122no—
203C22×C3×D3—122no—
204C22×C3×D3—124no—
205C22×C3×D3—124no—
206C22×C3×D3—122no—
207C22×C3×D3—122no—
208C32×D4—21no—
209C32×D4—22no—
210C32×D4—21no—
211C32×D4—21no—
212C32×D4—22no—
213C32×D4—22no—
214C32×D4—22no—
215C32×D4—42no—
216C32×D4—41no—
217C32×D4—41no—
218C32×D4—42no—
219C32×D4D1212yescomplemented
220C32×D4#6712yescomplemented
221C32×D4#6712yescomplemented
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—41no—
226C2×C32×C4C22×D311yescharacteristic
227C2×C32×C4C22×D311yescharacteristic
228C2×C32×C4C22×D311yescharacteristic
229#638—24no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3#6711yescharacteristic
232C4⋊(C3⋊D3)—21no—
233C4⋊(C3⋊D3)—21no—
234C4⋊(C3⋊D3)—21no—
235C4⋊(C3⋊D3)#6712yescomplemented
236C4×C3⋊D3—21no—
237C4×C3⋊D3—21no—
238C3×#67—68no—
239C3×#67—64no—
240C3×#67—64no—
241C2×C3×Dic3—31no—
242C2×C3×Dic3—31no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3—61no—
246C2×C3×Dic3—121no—
247C3×D12—32no—
248C3×D12—32no—
249C3×D12—62no—
250C3×D12—62no—
251C3×D12—62no—
252C3×D12—61no—
253C3×D12—61no—
254C3×D12—61no—
255C3×D12—61no—
256C3×D12—61no—
257C3×D12—61no—
258C3×D12—121no—
259C3×C4×D3—62no—
260C3×C4×D3—62no—
261C3×C4×D3—61no—
262C3×C4×D3—61no—
263C3×C4×D3—61no—
264C3×C4×D3—61no—
265#626—122no—
266#626—122no—
267#625—122no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—62no—
271C3×C3⋊C8—61no—
272C3×C3⋊C8—61no—
273C3×C3⋊C8—61no—
274C3×C3⋊C8—61no—
275C3×C3⋊C8—121no—
276#447—271noSylow
277C2×C33—42no—
278C2×C33#12011yescharacteristic
279C2×C33C2×D811yescharacteristic
280C2×C33AGL(1,ℤ/8)11yescharacteristic
281C3×C3⋊D3—22no—
282C3×C3⋊D3—42no—
283C3×C3⋊D3—81no—
284C24×C3—181no—
285C23×D3—61no—
286C23×D3—61no—
287C23×D3—62no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—41no—
292C2×C3×D4—91no—
293C2×C3×D4—91no—
294C2×C3×D4—181no—
295C2×C3×D4—182no—
296C2×C3×D4—182no—
297C2×C3×D4D3211yescharacteristic
298C2×C3×D4D3211yescharacteristic
299C2×C3×D4D3211yescharacteristic
300C22×C3×C4—91no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—62no—
304C2×#67—181no—
305C2×#67—181no—
306D3×D4—62no—
307D3×D4—62no—
308D3×D4—64no—
309D3×D4—64no—
310D3×D4—62no—
311D3×D4—62no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—181no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—61no—
322C3×D8—182no—
323C2×C3×C8—91no—
324C2×C3×C8—91no—
325C3×C4⋊C4—91no—
326#217—181no—
327#213—64no—
328#213—62no—
329#213—62no—
330#213—182no—
331#213—182no—
332(C2×D3)⋊C4—181no—
333(C2×D3)⋊C4—181no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—61no—
337C2×C3⋊C8—31no—
338C2×C3⋊C8—31no—
339C2×C3⋊C8—31no—
340C2×C3⋊C8—31no—
341C2×C3⋊C8—61no—
342C2×C3⋊C8—61no—
343D24—182no—
344C22×C32—22no—
345C22×C32—24no—
346C22×C32—22no—
347C22×C32—22no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—41no—
352C22×C32—42no—
353C22×C32—42no—
354C22×C32—44no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32—42no—
358C22×C32—42no—
359C22×C32—41no—
360C22×C32—41no—
361C22×C32—41no—
362C22×C32—41no—
363C22×C32—81no—
364C22×C32—81no—
365C22×C32—81no—
366C22×C32—81no—
367C22×C32—82no—
368C22×C32—82no—
369C22×C32D3×D411yescharacteristic
370C22×C32D3×D411yescharacteristic
371C22×C32C2×#6711yescharacteristic
372C2×C3⋊D3—21no—
373C2×C3⋊D3—21no—
374C2×C3⋊D3—22no—
375C2×C3⋊D3—48no—
376C2×C3⋊D3—41no—
377C2×C3⋊D3—41no—
378C2×C3⋊D3—41no—
379C2×C3⋊D3—41no—
380C2×C3⋊D3—41no—
381C2×C3⋊D3#21312yescomplemented
382C2×C3×D3—32no—
383C2×C3×D3—32no—
384C2×C3×D3—62no—
385C2×C3×D3—62no—
386C2×C3×D3—62no—
387C2×C3×D3—61no—
388C2×C3×D3—61no—
389C2×C3×D3—61no—
390C2×C3×D3—61no—
391C2×C3×D3—64no—
392C2×C3×D3—62no—
393C2×C3×D3—62no—
394C2×C3×D3—1216no—
395C2×C3×D3—128no—
396C2×C3×D3—128no—
397C2×C3×D3—122no—
398C2×C3×D3—122no—
399C2×C3×D3—121no—
400C2×C3×D3—121no—
401C2×C3×D3—121no—
402C2×C3×D3—121no—
403C2×C3×D3—122no—
404C2×C3×D3—121no—
405C2×C3×D3—121no—
406C2×C3×D3—121no—
407C2×C3×D3—121no—
408C2×C3×D3—121no—
409C2×C3×D3—121no—
410C2×C3×D3—241no—
411C2×C3×D3—241no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C2×D1211yescharacteristic
421C32×C4D3×D411yescharacteristic
422C32×C4D3×D411yescharacteristic
423C32×C4C2×#6711yescharacteristic
424C32×C4C2×#6711yescharacteristic
425C32×C4C2×#6711yescharacteristic
426C3⋊Dic3—21no—
427C3⋊Dic3—41no—
428C3×Dic3—62no—
429C3×Dic3—61no—
430C3×Dic3—61no—
431C3×Dic3—121no—
432C3×Dic3—121no—
433C3×Dic3—241no—
434C22×D4—91no—
435C2×D8—91no—
436C2×D8—271no—
437#121—271no—
438#102—91no—
439#102—271no—
440C22⋊C8—271no—
441C33#44711yescharacteristic, complemented, Sylow
442C23×C3—22no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—42no—
449C23×C3—91no—
450C23×C3—184no—
451C23×C3—181no—
452C23×C3—181no—
453C23×C3—362no—
454C23×C3—362no—
455C22×D3—31no—
456C22×D3—31no—
457C22×D3—61no—
458C22×D3—62no—
459C22×D3—68no—
460C22×D3—64no—
461C22×D3—64no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—61no—
465C22×D3—61no—
466C22×D3—121no—
467C22×D3—122no—
468C22×D3—122no—
469C22×D3—124no—
470C22×D3—124no—
471C22×D3—122no—
472C22×D3—122no—
473C3×D4—22no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—22no—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4—41no—
481C3×D4—41no—
482C3×D4—42no—
483C3×D4—42no—
484C3×D4—92no—
485C3×D4—184no—
486C3×D4—181no—
487C3×D4—181no—
488C3×D4—181no—
489C3×D4#62512yescomplemented
490C3×D4#62612yescomplemented
491C3×D4#62612yescomplemented
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—41no—
496C2×C3×C4—91no—
497C2×C3×C4—181no—
498C2×C3×C4—181no—
499C2×C3×C4—181no—
500C2×C3×C4C2×D3211yescharacteristic
501C2×C3×C4C2×D3211yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503#67—68no—
504#67—64no—
505#67—64no—
506#67—362no—
507#67—362no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—121no—
514D12—32no—
515D12—32no—
516D12—62no—
517D12—62no—
518D12—62no—
519D12—61no—
520D12—61no—
521D12—61no—
522D12—61no—
523D12—61no—
524D12—61no—
525D12—121no—
526D12—362no—
527C4×D3—62no—
528C4×D3—62no—
529C4×D3—61no—
530C4×D3—61no—
531C4×D3—61no—
532C4×D3—61no—
533C3×C8—181no—
534C3×C8—181no—
535C3⋊C8—62no—
536C3⋊C8—61no—
537C3⋊C8—61no—
538C3⋊C8—61no—
539C3⋊C8—61no—
540C3⋊C8—121no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—41no—
551C2×C32—41no—
552C2×C32—41no—
553C2×C32—42no—
554C2×C32—44no—
555C2×C32—42no—
556C2×C32—42no—
557C2×C32—82no—
558C2×C32—82no—
559C2×C32—84no—
560C2×C32#88211yescharacteristic
561C2×C32D3×D811yescharacteristic
562C2×C32D3×D811yescharacteristic
563C2×C32#91111yescharacteristic
564C2×C32#91411yescharacteristic
565C2×C32C2×#21311yescharacteristic
566C2×C32#93211yescharacteristic
567C2×C32#93711yescharacteristic
568C2×C32#95311yescharacteristic
569C3⋊D3—22no—
570C3⋊D3—42no—
571C3⋊D3—81no—
572C3×D3—64no—
573C3×D3—62no—
574C3×D3—62no—
575C3×D3—124no—
576C3×D3—122no—
577C3×D3—122no—
578C3×D3—242no—
579C3×D3—241no—
580C3×D3—241no—
581C24—181no—
582C2×D4—91no—
583C2×D4—91no—
584C2×D4—181no—
585C2×D4—182no—
586C2×D4—182no—
587C2×D4—541no—
588C2×D4#111311yescharacteristic
589C22×C4—91no—
590D8—182no—
591D8—542no—
592C2×C8—91no—
593C2×C8—91no—
594C4⋊C4—91no—
595C22⋊C4—541no—
596C22×C3—24no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—44no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—82no—
620C22×C3—82no—
621C22×C3—92no—
622C22×C3—181no—
623C22×C3—181no—
624C22×C3—182no—
625C22×C3—368no—
626C22×C3—361no—
627C22×C3—361no—
628C22×C3—361no—
629C22×C3—361no—
630C22×C3—361no—
631C22×C3D3×#6711yescharacteristic
632C22×C3D3×#6711yescharacteristic
633C22×C3#381111yescharacteristic
634C2×D3—32no—
635C2×D3—32no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—64no—
644C2×D3—62no—
645C2×D3—62no—
646C2×D3—1216no—
647C2×D3—128no—
648C2×D3—128no—
649C2×D3—122no—
650C2×D3—122no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—122no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—181no—
673C3×C4—361no—
674C3×C4C2×#62511yescharacteristic
675C3×C4C2×#62611yescharacteristic
676C3×C4C2×#62611yescharacteristic
677C3×C4D3×#6711yescharacteristic
678C3×C4D3×#6711yescharacteristic
679C3×C4#381111yescharacteristic
680Dic3—62no—
681Dic3—61no—
682Dic3—61no—
683Dic3—121no—
684Dic3—121no—
685Dic3—241no—
686C32—21no—
687C32—21no—
688C32—21no—
689C32—41no—
690C32#477311yescharacteristic, complemented
691C32#515611yescharacteristic, complemented
692C32#521711yescharacteristic, complemented
693C23—21no—
694C23—91no—
695C23—184no—
696C23—181no—
697C23—181no—
698C23—362no—
699C23—362no—
700D4—21no—
701D4—92no—
702D4—184no—
703D4—181no—
704D4—181no—
705D4—181no—
706D4—1082no—
707D4#629512yescomplemented
708C2×C4—91no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4C2×#111311yescharacteristic
713C8—181no—
714C8—181no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—44no—
725C2×C3—42no—
726C2×C3—42no—
727C2×C3—42no—
728C2×C3—41no—
729C2×C3—41no—
730C2×C3—41no—
731C2×C3—82no—
732C2×C3—82no—
733C2×C3—84no—
734C2×C3—182no—
735C2×C3—362no—
736C2×C3—721no—
737C2×C3D3×#21311yescharacteristic
738C2×C3D3×#21311yescharacteristic
739C2×C3#6392611yescharacteristic
740C2×C3#6393211yescharacteristic
741C2×C3#6393411yescharacteristic
742C2×C3#6393711yescharacteristic
743C2×C3#6397611yescharacteristic
744C2×C3#6397711yescharacteristic
745C2×C3#6398111yescharacteristic
746D3—64no—
747D3—62no—
748D3—62no—
749D3—124no—
750D3—122no—
751D3—122no—
752D3—242no—
753D3—241no—
754D3—241no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—92no—
759C22—181no—
760C22—181no—
761C22—182no—
762C22—368no—
763C22—361no—
764C22—361no—
765C22—361no—
766C22—361no—
767C22—361no—
768C22#8904911yescharacteristic
769C4—181no—
770C4—361no—
771C4C2×#629511yescharacteristic
772C4#8904911yescharacteristic
773C3—21no—
774C3—21no—
775C3—21no—
776C3—41no—
777C3#1059144711yescharacteristic, complemented
778C3#1059144811yescharacteristic, complemented
779C3#1059145611yescharacteristic, complemented
780C2—42no—
781C2—182no—
782C2—362no—
783C2—721no—
784C2#1172370211yescharacteristic
785C2#1172370611yescharacteristic
786C2#1172372711yescharacteristic
subgroupG/H
centerC22#89049
commutator, cosocleC2×C33×C4C23
FrattiniC2×C4C2×#1113
FittingC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×D4#1113
hypocenterC33#447
LCSG ▷ C2×C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C2×C3×#3753C2semidirect
3. #11723696C2semidirect
4. C2×#88810C2semidirect
5. C3×#63659C2semidirect
6. #11722075C2semidirect
7. #11722072C2semidirect
17. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. C3×C4⋊(C3⋊Dic3)C22semidirect
22. C2×C3×C3⋊(C3⋊C8)C22semidirect
23. C2×C3×C3⋊(C3⋊C8)C22semidirect
26. C2×D4×C3⋊D3D3semidirect
30. C2×#3753D3semidirect
40. #63659D3semidirect
58. C33×D4D4semidirect
66. C3×C4⋊(C3⋊D3)D4semidirect
90. C2×C4⋊(C3⋊D3)C2×D3semidirect
114. C4⋊(C3⋊Dic3)C2×D3semidirect
115. C2×C3⋊(C3⋊C8)C2×D3semidirect
116. C2×C3⋊(C3⋊C8)C2×D3semidirect
148. C2×C3×C3⋊D3D8semidirect
219. C32×D4D12semidirect
220. C32×D4#67semidirect
221. C32×D4#67semidirect
235. C4⋊(C3⋊D3)#67semidirect
381. C2×C3⋊D3#213semidirect
441. C33#447semidirect
489. C3×D4#625semidirect
490. C3×D4#626semidirect
491. C3×D4#626semidirect
690. C32#4773semidirect
691. C32#5156semidirect
692. C32#5217semidirect
707. D4#6295semidirect
777. C3#10591447semidirect
778. C3#10591448semidirect
779. C3#10591456semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×C3×#37532
#117236962
C2×#888102
C3×#636592
#117220752
#117220722
#105914563
#105914483
#105914473