Finite Group Databasebeta

← #13161459

Subgroups — #13161459

Order 1728.

2876 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6312C211yesmaximal, characteristic, complemented
2C22×C3×#638C211yesmaximal, characteristic, complemented
3C22×#6292C211yesmaximal, characteristic, complemented
4C2×C32×#217C211yesmaximal, characteristic, complemented
5C2×#88804C211yesmaximal, characteristic, complemented
6C2×#88803C211yesmaximal, characteristic, complemented
7#11722061C211yesmaximal, characteristic, complemented
8#10592659—31nomaximal
9#10591724—34nomaximal
10C24×C33C2211yescharacteristic
11C23×C3⋊(C3⋊D3)C2211yescharacteristic
12C23×C3×C3⋊D3C2211yescharacteristic
13C2×#6312—22no—
14C2×#6312—22no—
15C2×#6312—22no—
16C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×#638—22no—
18C2×C3×#638—22no—
19C2×C3×#638—22no—
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6292—22no—
24C2×#6292—22no—
25C2×#6292—22no—
26C32×#217—22no—
27#88804—22no—
28#88803—22no—
29C22×#638—31no—
30C22×#638—34no—
31C22×#638—64no—
32C22×#638D311yescharacteristic, complemented
33C22×C4⋊(C3⋊D3)—31no—
34C22×C3×#67—34no—
35C22×#626—34no—
36C2×C32×C22⋊C4—31no—
37C2×#3752—31no—
38C2×#3752—31no—
39C2×C3×#217D314yescomplemented
40C2×#3722—34no—
41C2×(C2×D3)⋊Dic3—34no—
42#63658—31no—
43#63579—34no—
44C23×C33—21no—
45C23×C33—21no—
46C23×C33—21no—
47C23×C33—21no—
48C23×C33—21no—
49C23×C33—21no—
50C23×C33D412yescomplemented
51C23×C33C2311yescharacteristic
52C22×C3⋊(C3⋊D3)—21no—
53C22×C3⋊(C3⋊D3)—21no—
54C22×C3⋊(C3⋊D3)—21no—
55C22×C3⋊(C3⋊D3)—21no—
56C22×C3⋊(C3⋊D3)—21no—
57C22×C3⋊(C3⋊D3)—21no—
58C22×C3⋊(C3⋊D3)D412yescomplemented
59C22×C3×C3⋊D3—21no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3—21no—
62C22×C3×C3⋊D3—21no—
63C22×C3×C3⋊D3—21no—
64C22×C3×C3⋊D3—21no—
65C22×C3×C3⋊D3D412yescomplemented
66#6312—28no—
67C2×C3⋊(C3⋊Dic3)—21no—
68C2×C3⋊(C3⋊Dic3)—21no—
69C2×C3⋊(C3⋊Dic3)D412yescomplemented
70C3×#638—28no—
71C2×C3×C3⋊Dic3—21no—
72C2×C3×C3⋊Dic3—21no—
73C2×C3×C3⋊Dic3D412yescomplemented
74C2×C32×Dic3—21no—
75C2×C32×Dic3—21no—
76C2×C32×Dic3—21no—
77C2×C32×Dic3—21no—
78C2×C32×Dic3—21no—
79C2×C32×Dic3D412yescomplemented
80#6292—28no—
81#5223—91no—
82#4960—94no—
83C24×C32—24no—
84C24×C32C2×D314yes—
85C24×C32C2×D311yescharacteristic
86C23×C3⋊D3—31no—
87C23×C3⋊D3—34no—
88C23×C3⋊D3—64no—
89C23×C3⋊D3C2×D311yescharacteristic
90C23×C3×D3—34no—
91C22×C32×C4—31no—
92C22×C32×C4—31no—
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—62no—
97C2×#638—68no—
98C2×#638—62no—
99C2×#638—68no—
100C2×#638—616no—
101C2×#638—616no—
102C2×#638—616no—
103C2×#638—68no—
104C2×#638—62no—
105C22×C3⋊Dic3—31no—
106C22×C3⋊Dic3—34no—
107C22×C3⋊Dic3—64no—
108C22×C3⋊Dic3C2×D311yescharacteristic
109C2×C4⋊(C3⋊D3)—62no—
110C2×C4⋊(C3⋊D3)—62no—
111C2×C4⋊(C3⋊D3)—62no—
112C2×C3×#67—68no—
113C2×C3×#67—68no—
114C2×C3×#67—68no—
115C22×C3×Dic3—34no—
116C22×C3×Dic3C2×D314yes—
117C22×C3×Dic3C2×D314yes—
118C2×#626—68no—
119C2×#626—68no—
120C2×#626—68no—
121C32×C22⋊C4—62no—
122#3752—62no—
123#3752—62no—
124C3×#217—28no—
125#3722—68no—
126(C2×D3)⋊Dic3—68no—
127C22×C33—22no—
128C22×C33—22no—
129C22×C33—22no—
130C22×C33—41no—
131C22×C33—41no—
132C22×C33—41no—
133C22×C33—41no—
134C22×C33C2×D411yescharacteristic
135C22×C33C2×D411yescharacteristic
136C22×C33C2×D411yescharacteristic
137C22×C33C2×D411yescharacteristic
138C22×C33C2×D411yescharacteristic
139C22×C33C2×D411yescharacteristic
140C22×C33#4111yescharacteristic
141C2×C3⋊(C3⋊D3)—22no—
142C2×C3⋊(C3⋊D3)—22no—
143C2×C3⋊(C3⋊D3)—22no—
144C2×C3⋊(C3⋊D3)—41no—
145C2×C3⋊(C3⋊D3)—41no—
146C2×C3⋊(C3⋊D3)—41no—
147C2×C3⋊(C3⋊D3)—41no—
148C2×C3×C3⋊D3—22no—
149C2×C3×C3⋊D3—22no—
150C2×C3×C3⋊D3—22no—
151C2×C3×C3⋊D3—41no—
152C2×C3×C3⋊D3—41no—
153C2×C3×C3⋊D3—41no—
154C2×C3×C3⋊D3—41no—
155C3⋊(C3⋊Dic3)—22no—
156C3×C3⋊Dic3—22no—
157C32×Dic3—22no—
158C32×Dic3—41no—
159C22×C3×D4—91no—
160C22×#67—34no—
161C22×#67—94no—
162C22×#67—91no—
163C22×#67—91no—
164C22×#67—184no—
165C22×D12—94no—
166C2×C3×C22⋊C4—34no—
167C2×#217—91no—
168C2×#217C3⋊D311yescharacteristic, complemented
169C2×(C2×D3)⋊C4—94no—
170C2×(C2×D3)⋊C4—94no—
171C2×(C2×D3)⋊C4—91no—
172C3⋊#95—94no—
173C3⋊#95—91no—
174C23×C32—28no—
175C23×C32—28no—
176C23×C32—21no—
177C23×C32—24no—
178C23×C32—24no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—28no—
185C23×C32—24no—
186C23×C32—24no—
187C23×C32—24no—
188C23×C32—24no—
189C23×C32—24no—
190C23×C32—44no—
191C23×C32—44no—
192C23×C32—44no—
193C23×C32—44no—
194C23×C32D1218yescomplemented
195C23×C32#6712yescomplemented
196C23×C32C22×D314yes—
197C23×C32C22×D311yescharacteristic
198C22×C3⋊D3—21no—
199C22×C3⋊D3—21no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—21no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3—32no—
205C22×C3⋊D3—38no—
206C22×C3⋊D3—68no—
207C22×C3⋊D3—68no—
208C22×C3⋊D3—68no—
209C22×C3⋊D3—64no—
210C22×C3⋊D3—61no—
211C22×C3⋊D3—64no—
212C22×C3⋊D3—61no—
213C22×C3⋊D3—61no—
214C22×C3⋊D3—61no—
215C22×C3⋊D3—61no—
216C22×C3⋊D3—61no—
217C22×C3⋊D3—64no—
218C22×C3⋊D3—64no—
219C22×C3⋊D3—64no—
220C22×C3⋊D3—64no—
221C22×C3⋊D3—124no—
222C22×C3⋊D3—124no—
223C22×C3⋊D3—124no—
224C22×C3⋊D3—124no—
225C22×C3⋊D3#6712yescomplemented
226C22×C3×D3—38no—
227C22×C3×D3—64no—
228C22×C3×D3—64no—
229C22×C3×D3—64no—
230C22×C3×D3—64no—
231C22×C3×D3—64no—
232C22×C3×D3—64no—
233C2×C32×C4—32no—
234C2×C32×C4—61no—
235C2×C32×C4—61no—
236C2×C32×C4—61no—
237C2×C32×C4—61no—
238C2×C32×C4—61no—
239#638—28no—
240#638—664no—
241#638—632no—
242#638—68no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—32no—
246C2×C3⋊Dic3—38no—
247C2×C3⋊Dic3—68no—
248C2×C3⋊Dic3—68no—
249C2×C3⋊Dic3—68no—
250C2×C3⋊Dic3—64no—
251C2×C3⋊Dic3—64no—
252C2×C3⋊Dic3—61no—
253C2×C3⋊Dic3—61no—
254C2×C3⋊Dic3#6712yescomplemented
255C4⋊(C3⋊D3)—68no—
256C3×#67—632no—
257C2×C3×Dic3—24no—
258C2×C3×Dic3—24no—
259C2×C3×Dic3—24no—
260C2×C3×Dic3—24no—
261C2×C3×Dic3—24no—
262C2×C3×Dic3—38no—
263C2×C3×Dic3—64no—
264C2×C3×Dic3—64no—
265C2×C3×Dic3#6718yescomplemented
266#626—632no—
267#392—271noSylow
268C2×C33—42no—
269C2×C33#12011yescharacteristic
270C2×C33#12011yescharacteristic
271C2×C33#12011yescharacteristic
272C2×C33#12111yescharacteristic
273C2×C33#12111yescharacteristic
274C2×C33#12111yescharacteristic
275C2×C33#12711yescharacteristic
276C3⋊(C3⋊D3)—42no—
277C3×C3⋊D3—42no—
278C24×C3—24no—
279C24×C3—91no—
280C24×C3D3214yes—
281C24×C3C2×C3⋊D311yescharacteristic
282C23×D3—34no—
283C23×D3—94no—
284C23×D3—91no—
285C23×D3—184no—
286C2×C3×D4—182no—
287C2×C3×D4—182no—
288C2×C3×D4—182no—
289C22×C3×C4—34no—
290C22×C3×C4—34no—
291C22×C3×C4—91no—
292C2×#67—68no—
293C2×#67—68no—
294C2×#67—68no—
295C2×#67—182no—
296C2×#67—182no—
297C2×#67—188no—
298C2×#67—182no—
299C2×#67—188no—
300C2×#67—182no—
301C2×#67—1816no—
302C2×#67—1816no—
303C2×#67—1816no—
304C2×#67—188no—
305C2×#67—182no—
306C2×#67—182no—
307C22×Dic3—34no—
308C22×Dic3—94no—
309C22×Dic3—91no—
310C22×Dic3—184no—
311C22×Dic3C2×C3⋊D311yescharacteristic
312C22×Dic3C2×C3⋊D311yescharacteristic
313C2×D12—188no—
314C2×D12—188no—
315C2×D12—188no—
316C3×C22⋊C4—68no—
317#217—22no—
318#217—182no—
319(C2×D3)⋊C4—182no—
320(C2×D3)⋊C4—188no—
321(C2×D3)⋊C4—188no—
322C22×C32—216no—
323C22×C32—28no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—24no—
330C22×C32—24no—
331C22×C32—24no—
332C22×C32—24no—
333C22×C32—24no—
334C22×C32—28no—
335C22×C32—28no—
336C22×C32—48no—
337C22×C32—48no—
338C22×C32—48no—
339C22×C32—48no—
340C22×C32—48no—
341C22×C32—48no—
342C22×C32—44no—
343C22×C32—44no—
344C22×C32—44no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32—41no—
348C22×C32—44no—
349C22×C32—41no—
350C22×C32C2×D1214yes—
351C22×C32#23514yes—
352C22×C32D3×D414yes—
353C22×C32D3×D414yes—
354C22×C32D3×D414yes—
355C22×C32D3×D414yes—
356C22×C32D3×D411yescharacteristic
357C22×C32D3×D411yescharacteristic
358C22×C32D3×D411yescharacteristic
359C22×C32#23711yescharacteristic
360C22×C32C2×#6714yes—
361C22×C32C2×#6711yescharacteristic
362C22×C32C2×#6711yescharacteristic
363C22×C32C2×#6711yescharacteristic
364C2×C3⋊D3—22no—
365C2×C3⋊D3—22no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—41no—
368C2×C3⋊D3—41no—
369C2×C3⋊D3—41no—
370C2×C3⋊D3—41no—
371C2×C3⋊D3—616no—
372C2×C3⋊D3—68no—
373C2×C3⋊D3—62no—
374C2×C3⋊D3—62no—
375C2×C3⋊D3—62no—
376C2×C3⋊D3—68no—
377C2×C3⋊D3—68no—
378C2×C3⋊D3—128no—
379C2×C3⋊D3—128no—
380C2×C3⋊D3—128no—
381C2×C3⋊D3—128no—
382C2×C3⋊D3—128no—
383C2×C3⋊D3—128no—
384C2×C3⋊D3—124no—
385C2×C3⋊D3—124no—
386C2×C3⋊D3—124no—
387C2×C3⋊D3—121no—
388C2×C3⋊D3—121no—
389C2×C3⋊D3—124no—
390C2×C3⋊D3—121no—
391C2×C3⋊D3—121no—
392C2×C3×D3—68no—
393C2×C3×D3—68no—
394C2×C3×D3—68no—
395C2×C3×D3—124no—
396C2×C3×D3—124no—
397C2×C3×D3—124no—
398C2×C3×D3—124no—
399C32×C4—62no—
400C32×C4—121no—
401C3⋊Dic3—22no—
402C3⋊Dic3—616no—
403C3⋊Dic3—68no—
404C3⋊Dic3—62no—
405C3×Dic3—28no—
406C3×Dic3—44no—
407C3×Dic3—68no—
408C22×D4—91no—
409C22×D4—271no—
410C22×D4—271no—
411C2×C22⋊C4—31no—
412C2×C22⋊C4—271no—
413C2×C22⋊C4—271no—
414#95—271no—
415C33#39211yescharacteristic, complemented, Sylow
416C23×C3—28no—
417C23×C3—28no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—28no—
431C23×C3—24no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3—44no—
435C23×C3—44no—
436C23×C3—92no—
437C23×C3—181no—
438C23×C3—181no—
439C23×C3—181no—
440C23×C3—181no—
441C23×C3—181no—
442C23×C3—181no—
443C23×C3#62618yescomplemented
444C23×C3C4⋊(C3⋊D3)12yescomplemented
445C23×C3C2×D3214yes—
446C23×C3C22×C3⋊D311yescharacteristic
447C22×D3—38no—
448C22×D3—64no—
449C22×D3—64no—
450C22×D3—64no—
451C22×D3—64no—
452C22×D3—64no—
453C22×D3—64no—
454C22×D3—98no—
455C22×D3—92no—
456C22×D3—188no—
457C22×D3—188no—
458C22×D3—188no—
459C22×D3—184no—
460C22×D3—184no—
461C22×D3—184no—
462C22×D3—184no—
463C22×D3—184no—
464C22×D3—184no—
465C22×D3—181no—
466C22×D3—181no—
467C22×D3—181no—
468C22×D3—181no—
469C22×D3—181no—
470C22×D3—181no—
471C22×D3—364no—
472C22×D3—364no—
473C22×D3—364no—
474C22×D3—364no—
475C3×D4—188no—
476C2×C3×C4—38no—
477C2×C3×C4—64no—
478C2×C3×C4—64no—
479C2×C3×C4—64no—
480C2×C3×C4—64no—
481C2×C3×C4—64no—
482C2×C3×C4—92no—
483C2×C3×C4—181no—
484C2×C3×C4—181no—
485#67—632no—
486#67—188no—
487#67—1864no—
488#67—188no—
489#67—1832no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—38no—
496C2×Dic3—64no—
497C2×Dic3—64no—
498C2×Dic3—98no—
499C2×Dic3—92no—
500C2×Dic3—188no—
501C2×Dic3—188no—
502C2×Dic3—188no—
503C2×Dic3—184no—
504C2×Dic3—184no—
505C2×Dic3—181no—
506C2×Dic3—181no—
507C2×Dic3#63812yescomplemented
508D12—1832no—
509C2×C32—24no—
510C2×C32—24no—
511C2×C32—24no—
512C2×C32—24no—
513C2×C32—24no—
514C2×C32—24no—
515C2×C32—24no—
516C2×C32—416no—
517C2×C32—48no—
518C2×C32—42no—
519C2×C32#88214yes—
520C2×C32#88214yes—
521C2×C32#88414yes—
522C2×C32#88414yes—
523C2×C32#93014yes—
524C2×C32#93714yes—
525C2×C32#93711yescharacteristic
526C2×C32#93711yescharacteristic
527C2×C32#93811yescharacteristic
528C2×C32#93911yescharacteristic
529C2×C32#93911yescharacteristic
530C2×C32#94014yes—
531C2×C32#94011yescharacteristic
532C2×C32#95311yescharacteristic
533C3⋊D3—42no—
534C3⋊D3—1216no—
535C3⋊D3—128no—
536C3⋊D3—122no—
537C3×D3—128no—
538C24—91no—
539C24—271no—
540C24D3×C3⋊D311yescharacteristic
541C2×D4—182no—
542C2×D4—182no—
543C2×D4—182no—
544C2×D4—542no—
545C2×D4—542no—
546C2×D4—542no—
547C2×D4—542no—
548C2×D4—542no—
549C2×D4—542no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—91no—
553C22×C4—271no—
554C22⋊C4—62no—
555C22⋊C4—542no—
556C22⋊C4—542no—
557C22×C3—216no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—28no—
562C22×C3—28no—
563C22×C3—28no—
564C22×C3—24no—
565C22×C3—24no—
566C22×C3—24no—
567C22×C3—24no—
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—24no—
571C22×C3—48no—
572C22×C3—48no—
573C22×C3—48no—
574C22×C3—48no—
575C22×C3—48no—
576C22×C3—48no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—182no—
586C22×C3—182no—
587C22×C3—182no—
588C22×C3—361no—
589C22×C3—361no—
590C22×C3—361no—
591C22×C3—361no—
592C22×C3#380414yes—
593C22×C3C2×#62614yes—
594C22×C3D3×#6714yes—
595C22×C3D3×#6714yes—
596C22×C3D3×#6714yes—
597C22×C3#381114yes—
598C22×C3#381114yes—
599C22×C3C2×C4⋊(C3⋊D3)11yescharacteristic
600C22×C3#382811yescharacteristic
601C22×C3D4×C3⋊D311yescharacteristic
602C22×C3D4×C3⋊D311yescharacteristic
603C22×C3D4×C3⋊D311yescharacteristic
604C22×C3D4×C3⋊D311yescharacteristic
605C22×C3C2×#63811yescharacteristic
606C2×D3—68no—
607C2×D3—68no—
608C2×D3—68no—
609C2×D3—124no—
610C2×D3—124no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—1816no—
614C2×D3—182no—
615C2×D3—182no—
616C2×D3—182no—
617C2×D3—188no—
618C2×D3—188no—
619C2×D3—188no—
620C2×D3—368no—
621C2×D3—368no—
622C2×D3—368no—
623C2×D3—368no—
624C2×D3—368no—
625C2×D3—368no—
626C2×D3—361no—
627C2×D3—361no—
628C2×D3—361no—
629C2×D3—361no—
630C2×D3—364no—
631C2×D3—364no—
632C2×D3—364no—
633C2×D3—364no—
634C3×C4—68no—
635C3×C4—124no—
636C3×C4—182no—
637Dic3—22no—
638Dic3—41no—
639Dic3—68no—
640Dic3—1816no—
641Dic3—182no—
642Dic3—188no—
643C32—24no—
644C32#496014yescomplemented
645C32#522311yescharacteristic, complemented
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—92no—
653C23—181no—
654C23—181no—
655C23—181no—
656C23—181no—
657C23—181no—
658C23—181no—
659C23—272no—
660C23—541no—
661C23—541no—
662C23—541no—
663C23—541no—
664C23—541no—
665C23—541no—
666C23#629212yescomplemented
667C23C2×D3×C3⋊D311yescharacteristic
668D4—188no—
669D4—548no—
670D4—548no—
671C2×C4—32no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—92no—
678C2×C4—181no—
679C2×C4—181no—
680C2×C4—272no—
681C2×C4—541no—
682C2×C4—541no—
683C2×C3—24no—
684C2×C3—24no—
685C2×C3—24no—
686C2×C3—24no—
687C2×C3—24no—
688C2×C3—24no—
689C2×C3—24no—
690C2×C3—416no—
691C2×C3—42no—
692C2×C3—48no—
693C2×C3—362no—
694C2×C3#6395814yes—
695C2×C3#6397114yes—
696C2×C3#6397714yes—
697C2×C3#6397814yes—
698C2×C3#6397914yes—
699C2×C3#6398114yes—
700C2×C3#6398314yes—
701C2×C3#6409111yescharacteristic
702C2×C3#6409111yescharacteristic
703C2×C3#6409311yescharacteristic
704C2×C3#6409311yescharacteristic
705C2×C3#6413911yescharacteristic
706C2×C3#6414611yescharacteristic
707C2×C3#6414911yescharacteristic
708D3—128no—
709D3—3616no—
710D3—362no—
711D3—368no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—182no—
720C22—182no—
721C22—182no—
722C22—361no—
723C22—361no—
724C22—361no—
725C22—361no—
726C22—542no—
727C22—542no—
728C22—542no—
729C22—1081no—
730C22—1081no—
731C22—1081no—
732C22—1081no—
733C22#8903111yescharacteristic
734C22C2×#629211yescharacteristic
735C22D3×#63811yescharacteristic
736C22C3⋊D3×#6711yescharacteristic
737C22C3⋊D3×#6711yescharacteristic
738C22#8903911yescharacteristic
739C22#8903911yescharacteristic
740C4—62no—
741C4—121no—
742C4—182no—
743C4—542no—
744C3—24no—
745C3#1059172414yescomplemented
746C3#1059265911yescharacteristic, complemented
747C2—42no—
748C2—362no—
749C2—1082no—
750C2#1172362311yescharacteristic
751C2#1172362411yescharacteristic
752C2#1172363211yescharacteristic
753C2#1172363311yescharacteristic
754C2#1172363611yescharacteristic
755C2#1172363911yescharacteristic
756C2#1172364311yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×C3⋊D3
commutator, socle, cosocleC23×C33C23
FittingC24×C33C22
hypercenterC24D3×C3⋊D3
hypocenterC33#392
LCSG ▷ C23×C33 ▷ C33
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×#6312C2semidirect
2. C22×C3×#638C2semidirect
3. C22×#6292C2semidirect
4. C2×C32×#217C2semidirect
5. C2×#88804C2semidirect
6. C2×#88803C2semidirect
7. #11722061C2semidirect
32. C22×#638D3semidirect
39. C2×C3×#217D3semidirect
50. C23×C33D4semidirect
58. C22×C3⋊(C3⋊D3)D4semidirect
65. C22×C3×C3⋊D3D4semidirect
69. C2×C3⋊(C3⋊Dic3)D4semidirect
73. C2×C3×C3⋊Dic3D4semidirect
79. C2×C32×Dic3D4semidirect
168. C2×#217C3⋊D3semidirect
194. C23×C32D12semidirect
195. C23×C32#67semidirect
225. C22×C3⋊D3#67semidirect
254. C2×C3⋊Dic3#67semidirect
265. C2×C3×Dic3#67semidirect
415. C33#392semidirect
443. C23×C3#626semidirect
444. C23×C3C4⋊(C3⋊D3)semidirect
507. C2×Dic3#638semidirect
644. C32#4960semidirect
645. C32#5223semidirect
666. C23#6292semidirect
745. C3#10591724semidirect
746. C3#10592659semidirect

Maximal subgroups

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

subgroupindex
C22×#63122
C22×C3×#6382
C22×#62922
C2×C32×#2172
C2×#888042
C2×#888032
#117220612
#105926593
#105917243