Finite Group Databasebeta

← #13162055

Subgroups — #13162055

Order 1728.

1882 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic
2C23×C3×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#3757C211yesmaximal, characteristic, complemented
4C2×#88814C212yesmaximal, complemented
5#11722082C212yesmaximal, complemented
6#10591713—31nomaximal
7#10591711—31nomaximal
8#10591710—31nomaximal
9C24×C33C2211yescharacteristic
10C23×C3×C3⋊D3C2211yescharacteristic
11C2×C3×#638—22no—
12C2×C3×#638—22no—
13C2×C3×#638C414yescomplemented
14C22×C3×C3⋊Dic3—22no—
15C22×C3×C3⋊Dic3—24no—
16C22×C3×C3⋊Dic3C2212yes—
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊Dic3C2212yes—
19C3×#3757—22no—
20#88814—24no—
21C22×#638D311yescharacteristic
22C23×C3⋊Dic3D311yescharacteristic, complemented
23C22×C3×#67—31no—
24C22×C3×#67—31no—
25C22×C3×#67—61no—
26C23×C3×Dic3—31no—
27C23×C3×Dic3—31no—
28C23×C3×Dic3—61no—
29C2×#3757D311yescharacteristic, complemented
30C2×C3×#217—31no—
31C2×C3×#217—31no—
32C2×C3×#217—61no—
33C2×#3722—32no—
34C2×(C2×D3)⋊Dic3—32no—
35C2×(C2×D3)⋊Dic3—32no—
36#63579—32no—
37#63579—32no—
38#63579—32no—
39C23×C33—22no—
40C23×C33—22no—
41C23×C33C2×C412yes—
42C23×C33D412yes—
43C23×C33D412yes—
44C23×C33C2311yescharacteristic
45C22×C3×C3⋊D3—21no—
46C22×C3×C3⋊D3—21no—
47C22×C3×C3⋊D3—22no—
48C22×C3×C3⋊D3—22no—
49C22×C3×C3⋊D3C2×C412yescomplemented
50C3×#638—28no—
51C2×C3×C3⋊Dic3—28no—
52C2×C3×C3⋊Dic3—22no—
53C2×C3×C3⋊Dic3—22no—
54C2×C3×C3⋊Dic3—21no—
55C2×C3×C3⋊Dic3—21no—
56C2×C3×C3⋊Dic3—22no—
57C2×C3×C3⋊Dic3—22no—
58C2×C3×C3⋊Dic3—22no—
59C2×C3×C3⋊Dic3C2×C412yescomplemented
60C2×C3×C3⋊Dic3D414yescomplemented
61#5220—91no—
62#5213—91no—
63#4958—91no—
64C24×C32—21no—
65C24×C32—21no—
66C24×C32—21no—
67C24×C32—41no—
68C24×C32C2×D311yescharacteristic
69C24×C32C2×D311yescharacteristic
70C24×C32C2×D311yescharacteristic
71C23×C3⋊D3C2×D311yescharacteristic
72C23×C3×D3—31no—
73C23×C3×D3—31no—
74C23×C3×D3—61no—
75C2×#638—22no—
76C2×#638—22no—
77C2×#638Dic314yescomplemented
78C22×C3⋊Dic3—22no—
79C22×C3⋊Dic3—24no—
80C22×C3⋊Dic3C2×D312yes—
81C22×C3⋊Dic3C2×D311yescharacteristic
82C22×C3⋊Dic3C2×D312yes—
83C2×C3×#67—34no—
84C2×C3×#67—34no—
85C2×C3×#67—64no—
86C2×C3×#67—64no—
87C2×C3×#67—64no—
88C2×C3×#67—62no—
89C2×C3×#67—62no—
90C2×C3×#67—62no—
91C2×C3×#67—62no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—32no—
95C22×C3×Dic3—32no—
96C22×C3×Dic3—32no—
97C22×C3×Dic3—32no—
98C22×C3×Dic3—64no—
99C22×C3×Dic3—64no—
100C22×C3×Dic3—62no—
101C22×C3×Dic3—61no—
102C22×C3×Dic3—68no—
103C22×C3×Dic3—64no—
104C22×C3×Dic3—62no—
105C22×C3×Dic3—62no—
106C22×C3×Dic3—62no—
107#3757—22no—
108C3×#217—64no—
109C3×#217—62no—
110C3×#217—62no—
111#3722—64no—
112(C2×D3)⋊Dic3—64no—
113(C2×D3)⋊Dic3—64no—
114C22×C33—24no—
115C22×C33—22no—
116C22×C33—24no—
117C22×C33—22no—
118C22×C33C22⋊C414yescomplemented
119C22×C33C22×C411yescharacteristic
120C22×C33C2×D411yescharacteristic
121C22×C33C2×D411yescharacteristic
122C22×C33C2×D412yes—
123C22×C33#4112yes—
124C2×C3×C3⋊D3—22no—
125C2×C3×C3⋊D3—24no—
126C2×C3×C3⋊D3—41no—
127C2×C3×C3⋊D3—42no—
128C2×C3×C3⋊D3—41no—
129C3×C3⋊Dic3—22no—
130C3×C3⋊Dic3—24no—
131C3×C3⋊Dic3—42no—
132C22×C3×D4—91no—
133C23×C3×C4—91no—
134C22×#67—31no—
135C22×#67—31no—
136C22×#67—61no—
137C23×Dic3—31no—
138C23×Dic3—31no—
139C23×Dic3—61no—
140C2×C3×C22⋊C4—91no—
141C2×#217—31no—
142C2×#217—31no—
143C2×#217—61no—
144C2×#217—92no—
145C2×(C2×D3)⋊C4—92no—
146C2×(C2×D3)⋊C4—92no—
147C3⋊#95—92no—
148C3⋊#95—92no—
149C3⋊#95—92no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32—24no—
153C23×C32—24no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32—22no—
158C23×C32—22no—
159C23×C32—22no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—42no—
171C23×C32—42no—
172C23×C32—42no—
173C23×C32—41no—
174C23×C32—42no—
175C23×C32—42no—
176C23×C32—42no—
177C23×C32—42no—
178C23×C32—44no—
179C23×C32—44no—
180C23×C32C4×D312yes—
181C23×C32C4×D312yes—
182C23×C32D1212yes—
183C23×C32D1212yes—
184C23×C32C2×Dic312yes—
185C23×C32#6712yes—
186C23×C32#6712yes—
187C23×C32#6712yes—
188C23×C32#6712yes—
189C23×C32C22×D311yescharacteristic
190C23×C32C22×D311yescharacteristic
191C23×C32C22×D311yescharacteristic
192C22×C3⋊D3—21no—
193C22×C3⋊D3—21no—
194C22×C3⋊D3—22no—
195C22×C3⋊D3—22no—
196C22×C3⋊D3C2×Dic312yescomplemented
197C22×C3×D3—32no—
198C22×C3×D3—32no—
199C22×C3×D3—62no—
200C22×C3×D3—62no—
201C22×C3×D3—62no—
202C22×C3×D3—61no—
203C22×C3×D3—61no—
204C22×C3×D3—62no—
205C22×C3×D3—62no—
206C22×C3×D3—62no—
207C22×C3×D3—62no—
208C22×C3×D3—61no—
209C22×C3×D3—61no—
210C22×C3×D3—122no—
211C22×C3×D3—122no—
212#638—28no—
213C2×C3⋊Dic3—28no—
214C2×C3⋊Dic3—22no—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3C2×Dic312yescomplemented
222C2×C3⋊Dic3#6714yescomplemented
223C3×#67—616no—
224C3×#67—68no—
225C3×#67—68no—
226C2×C3×Dic3—32no—
227C2×C3×Dic3—32no—
228C2×C3×Dic3—34no—
229C2×C3×Dic3—34no—
230C2×C3×Dic3—62no—
231C2×C3×Dic3—64no—
232C2×C3×Dic3—616no—
233C2×C3×Dic3—68no—
234C2×C3×Dic3—68no—
235C2×C3×Dic3—64no—
236C2×C3×Dic3—64no—
237C2×C3×Dic3—62no—
238C2×C3×Dic3—62no—
239C2×C3×Dic3—62no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—61no—
242C2×C3×Dic3—62no—
243C2×C3×Dic3—62no—
244C2×C3×Dic3—62no—
245C2×C3×Dic3—61no—
246C2×C3×Dic3—61no—
247C2×C3×Dic3—64no—
248C2×C3×Dic3—62no—
249C2×C3×Dic3—62no—
250C2×C3×Dic3—62no—
251C2×C3×Dic3—62no—
252C2×C3×Dic3—62no—
253C2×C3×Dic3—62no—
254C2×C3×Dic3—122no—
255C2×C3×Dic3—122no—
256#386—271noSylow
257C2×C33—24no—
258C2×C33C2×C22⋊C411yescharacteristic
259C2×C33C4×D412yes—
260C2×C33#12011yescharacteristic
261C2×C33#12112yes—
262C2×C33#12311yescharacteristic
263C3×C3⋊D3—42no—
264C24×C3—21no—
265C24×C3—21no—
266C24×C3—21no—
267C24×C3—41no—
268C24×C3—91no—
269C24×C3D3211yescharacteristic
270C24×C3D3211yescharacteristic
271C24×C3D3211yescharacteristic
272C23×D3—31no—
273C23×D3—31no—
274C23×D3—61no—
275C2×C3×D4—94no—
276C2×C3×D4—182no—
277C2×C3×D4—182no—
278C22×C3×C4—91no—
279C22×C3×C4—92no—
280C22×C3×C4—92no—
281C22×C3×C4—184no—
282C22×C3×C4—182no—
283C2×#67—34no—
284C2×#67—34no—
285C2×#67—64no—
286C2×#67—64no—
287C2×#67—64no—
288C2×#67—62no—
289C2×#67—62no—
290C2×#67—62no—
291C2×#67—62no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—32no—
295C22×Dic3—32no—
296C22×Dic3—32no—
297C22×Dic3—32no—
298C22×Dic3—62no—
299C22×Dic3—61no—
300C22×Dic3—62no—
301C22×Dic3—64no—
302C22×Dic3—64no—
303C22×Dic3—68no—
304C22×Dic3—64no—
305C22×Dic3—62no—
306C22×Dic3—62no—
307C3×C22⋊C4—182no—
308#217—64no—
309#217—62no—
310#217—62no—
311#217—184no—
312(C2×D3)⋊C4—184no—
313(C2×D3)⋊C4—184no—
314C22×C32—24no—
315C22×C32—22no—
316C22×C32—24no—
317C22×C32—22no—
318C22×C32—24no—
319C22×C32—24no—
320C22×C32—28no—
321C22×C32—28no—
322C22×C32—24no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—24no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—24no—
329C22×C32—24no—
330C22×C32—24no—
331C22×C32—24no—
332C22×C32—24no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—22no—
336C22×C32—22no—
337C22×C32—22no—
338C22×C32—21no—
339C22×C32—21no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—22no—
346C22×C32—22no—
347C22×C32—22no—
348C22×C32—44no—
349C22×C32—41no—
350C22×C32—41no—
351C22×C32—41no—
352C22×C32—42no—
353C22×C32—42no—
354C22×C32—44no—
355C22×C32—42no—
356C22×C32—42no—
357C22×C32—44no—
358C22×C32—42no—
359C22×C32—42no—
360C22×C32—44no—
361C22×C32—44no—
362C22×C32—44no—
363C22×C32—48no—
364C22×C32—48no—
365C22×C32—44no—
366C22×C32(C2×D3)⋊C414yescomplemented
367C22×C32(C2×D3)⋊C414yescomplemented
368C22×C32#21714yescomplemented
369C22×C32C2×C4×D311yescharacteristic
370C22×C32C2×C4×D311yescharacteristic
371C22×C32C2×D1211yescharacteristic
372C22×C32C2×D1211yescharacteristic
373C22×C32#23512yes—
374C22×C32D3×D412yes—
375C22×C32D3×D412yes—
376C22×C32#23712yes—
377C22×C32#23712yes—
378C22×C32C22×Dic311yescharacteristic
379C22×C32C2×#6711yescharacteristic
380C22×C32C2×#6711yescharacteristic
381C22×C32C2×#6711yescharacteristic
382C22×C32C2×#6711yescharacteristic
383C22×C32C2×#6712yes—
384C2×C3⋊D3—22no—
385C2×C3⋊D3—24no—
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C2×C3⋊D3—42no—
389C2×C3×D3—64no—
390C2×C3×D3—64no—
391C2×C3×D3—62no—
392C2×C3×D3—62no—
393C2×C3×D3—64no—
394C2×C3×D3—124no—
395C2×C3×D3—122no—
396C2×C3×D3—122no—
397C2×C3×D3—124no—
398C2×C3×D3—121no—
399C2×C3×D3—121no—
400C2×C3×D3—121no—
401C2×C3×D3—122no—
402C2×C3×D3—122no—
403C2×C3×D3—121no—
404C3⋊Dic3—22no—
405C3⋊Dic3—24no—
406C3⋊Dic3—42no—
407C3×Dic3—68no—
408C3×Dic3—64no—
409C3×Dic3—64no—
410C3×Dic3—62no—
411C3×Dic3—62no—
412C3×Dic3—64no—
413C3×Dic3—124no—
414C3×Dic3—122no—
415C3×Dic3—122no—
416C22×D4—91no—
417C23×C4—91no—
418C2×C22⋊C4—91no—
419C2×C22⋊C4—272no—
420#95—272no—
421C33#38611yescharacteristic, complemented, Sylow
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—42no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—44no—
447C23×C3—44no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3—42no—
451C23×C3—41no—
452C23×C3—92no—
453C23×C3—182no—
454C23×C3—181no—
455C23×C3—181no—
456C23×C3—182no—
457C23×C3D3×Dic312yes—
458C23×C3D3×Dic312yes—
459C23×C3#62412yes—
460C23×C3#62512yes—
461C23×C3#62512yes—
462C23×C3#62612yes—
463C23×C3#62612yes—
464C23×C3#62612yes—
465C23×C3#62612yes—
466C23×C3C2×D3211yescharacteristic
467C23×C3C2×D3211yescharacteristic
468C23×C3C2×D3211yescharacteristic
469C22×D3—32no—
470C22×D3—32no—
471C22×D3—62no—
472C22×D3—62no—
473C22×D3—62no—
474C22×D3—62no—
475C22×D3—62no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—62no—
481C22×D3—62no—
482C22×D3—122no—
483C22×D3—122no—
484C3×D4—188no—
485C2×C3×C4—92no—
486C2×C3×C4—94no—
487C2×C3×C4—188no—
488C2×C3×C4—182no—
489C2×C3×C4—181no—
490C2×C3×C4—181no—
491C2×C3×C4—182no—
492C2×C3×C4—182no—
493C2×C3×C4—182no—
494C2×C3×C4—182no—
495#67—616no—
496#67—68no—
497#67—68no—
498C2×Dic3—32no—
499C2×Dic3—32no—
500C2×Dic3—34no—
501C2×Dic3—34no—
502C2×Dic3—62no—
503C2×Dic3—64no—
504C2×Dic3—616no—
505C2×Dic3—68no—
506C2×Dic3—68no—
507C2×Dic3—64no—
508C2×Dic3—64no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—62no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—64no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—62no—
523C2×Dic3—62no—
524C2×Dic3—62no—
525C2×Dic3—62no—
526C2×Dic3—122no—
527C2×Dic3—122no—
528C2×C32—24no—
529C2×C32—28no—
530C2×C32—24no—
531C2×C32—24no—
532C2×C32—22no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—21no—
539C2×C32—22no—
540C2×C32—22no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—22no—
544C2×C32—22no—
545C2×C32—22no—
546C2×C32—21no—
547C2×C32—41no—
548C2×C32—42no—
549C2×C32—41no—
550C2×C32—42no—
551C2×C32—41no—
552C2×C32—44no—
553C2×C32—44no—
554C2×C32—48no—
555C2×C32#67⋊C412yes—
556C2×C32#88211yescharacteristic
557C2×C32#88611yescharacteristic
558C2×C32C2×(C2×D3)⋊C411yescharacteristic
559C2×C32C2×(C2×D3)⋊C411yescharacteristic
560C2×C32C4×#6712yes—
561C2×C32#92911yescharacteristic
562C2×C32#93012yes—
563C2×C32D4×Dic312yes—
564C2×C32#93511yescharacteristic
565C2×C32#93711yescharacteristic
566C2×C32#93912yes—
567C2×C32#93912yes—
568C2×C32C2×#21711yescharacteristic
569C2×C32#95311yescharacteristic
570C3⋊D3—42no—
571C3×D3—124no—
572C3×D3—122no—
573C3×D3—122no—
574C24—91no—
575C24#111311yescharacteristic
576C2×D4—94no—
577C2×D4—182no—
578C2×D4—182no—
579C22×C4—91no—
580C22×C4—92no—
581C22×C4—92no—
582C22×C4—184no—
583C22×C4—182no—
584C22⋊C4—182no—
585C22⋊C4—544no—
586C22×C3—24no—
587C22×C3—28no—
588C22×C3—24no—
589C22×C3—28no—
590C22×C3—24no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—22no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—24no—
618C22×C3—24no—
619C22×C3—24no—
620C22×C3—44no—
621C22×C3—44no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—44no—
625C22×C3—44no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—48no—
629C22×C3—44no—
630C22×C3—48no—
631C22×C3—44no—
632C22×C3—41no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—42no—
637C22×C3—44no—
638C22×C3—184no—
639C22×C3—182no—
640C22×C3—361no—
641C22×C3—361no—
642C22×C3—362no—
643C22×C3(C2×D3)⋊Dic314yescomplemented
644C22×C3(C2×D3)⋊Dic314yescomplemented
645C22×C3#372214yescomplemented
646C22×C3C2×D3×Dic311yescharacteristic
647C22×C3C2×D3×Dic311yescharacteristic
648C22×C3#380412yes—
649C22×C3#380412yes—
650C22×C3#380512yes—
651C22×C3C2×#62411yescharacteristic
652C22×C3C2×#62511yescharacteristic
653C22×C3C2×#62511yescharacteristic
654C22×C3C2×#62611yescharacteristic
655C22×C3C2×#62611yescharacteristic
656C22×C3C2×#62611yescharacteristic
657C22×C3C2×#62611yescharacteristic
658C22×C3D3×#6712yes—
659C22×C3D3×#6712yes—
660C22×C3#381112yes—
661C2×D3—64no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—64no—
665C2×D3—64no—
666C2×D3—124no—
667C2×D3—124no—
668C2×D3—122no—
669C2×D3—122no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—122no—
674C2×D3—122no—
675C2×D3—121no—
676C3×C4—182no—
677C3×C4—184no—
678C3×C4—362no—
679Dic3—68no—
680Dic3—64no—
681Dic3—62no—
682Dic3—62no—
683Dic3—64no—
684Dic3—64no—
685Dic3—124no—
686Dic3—122no—
687Dic3—122no—
688C32—21no—
689C32—21no—
690C32—21no—
691C32—41no—
692C32#495811yescharacteristic, complemented
693C32#521311yescharacteristic, complemented
694C32#522011yescharacteristic, complemented
695C23—22no—
696C23—22no—
697C23—92no—
698C23—182no—
699C23—181no—
700C23—181no—
701C23—182no—
702C23#629412yes—
703C23#629512yes—
704C23#629512yes—
705C23C2×#111311yescharacteristic
706D4—188no—
707C2×C4—92no—
708C2×C4—94no—
709C2×C4—188no—
710C2×C4—182no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—182no—
714C2×C4—182no—
715C2×C4—182no—
716C2×C4—182no—
717C2×C3—28no—
718C2×C3—24no—
719C2×C3—24no—
720C2×C3—24no—
721C2×C3—22no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3—22no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—44no—
737C2×C3—44no—
738C2×C3—48no—
739C2×C3—42no—
740C2×C3—41no—
741C2×C3—41no—
742C2×C3—42no—
743C2×C3—41no—
744C2×C3—362no—
745C2×C3#6395212yes—
746C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
747C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
748C2×C3#6396111yescharacteristic
749C2×C3#6396211yescharacteristic
750C2×C3C2×#372211yescharacteristic
751C2×C3#6396611yescharacteristic
752C2×C3Dic3×#6712yes—
753C2×C3#67⋊Dic312yes—
754C2×C3#6397611yescharacteristic
755C2×C3#6397711yescharacteristic
756C2×C3#6397812yes—
757C2×C3#6397812yes—
758C2×C3#6398012yes—
759C2×C3#6398111yescharacteristic
760D3—124no—
761D3—122no—
762D3—122no—
763C22—24no—
764C22—22no—
765C22—24no—
766C22—22no—
767C22—182no—
768C22—184no—
769C22—362no—
770C22—361no—
771C22—361no—
772C22#8881414yescomplemented
773C22C2×#629411yescharacteristic
774C22#8904612yes—
775C22C2×#629511yescharacteristic
776C22C2×#629511yescharacteristic
777C22#8904912yes—
778C4—182no—
779C4—184no—
780C4—362no—
781C3—21no—
782C3—21no—
783C3—21no—
784C3—41no—
785C3#1059171011yescharacteristic, complemented
786C3#1059171111yescharacteristic, complemented
787C3#1059171311yescharacteristic, complemented
788C2—24no—
789C2—362no—
790C2#1172371712yes—
791C2C2×#8881411yescharacteristic
792C2#1172372011yescharacteristic
793C2#1172372612yes—
794C2#1172372711yescharacteristic
subgroupG/H
center, FrattiniC23C2×#1113
commutatorC22×C33C22×C4
FittingC24×C33C22
socle, cosocleC23×C33C23
prime radicalC22×C3×#638C2
hypercenterC24#1113
hypocenterC33#386
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C23×C3×C3⋊Dic3C2semidirect
3. C2×C3×#3757C2semidirect
4. C2×#88814C2semidirect
5. #11722082C2semidirect
13. C2×C3×#638C4semidirect
22. C23×C3⋊Dic3D3semidirect
29. C2×#3757D3semidirect
49. C22×C3×C3⋊D3C2×C4semidirect
59. C2×C3×C3⋊Dic3C2×C4semidirect
60. C2×C3×C3⋊Dic3D4semidirect
77. C2×#638Dic3semidirect
118. C22×C33C22⋊C4semidirect
196. C22×C3⋊D3C2×Dic3semidirect
221. C2×C3⋊Dic3C2×Dic3semidirect
222. C2×C3⋊Dic3#67semidirect
366. C22×C32(C2×D3)⋊C4semidirect
367. C22×C32(C2×D3)⋊C4semidirect
368. C22×C32#217semidirect
421. C33#386semidirect
643. C22×C3(C2×D3)⋊Dic3semidirect
644. C22×C3(C2×D3)⋊Dic3semidirect
645. C22×C3#3722semidirect
692. C32#4958semidirect
693. C32#5213semidirect
694. C32#5220semidirect
772. C22#88814semidirect
785. C3#10591710semidirect
786. C3#10591711semidirect
787. C3#10591713semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C23×C3×C3⋊Dic32
C2×C3×#37572
C2×#888142
#117220822
#105917133
#105917113
#105917103