Finite Group Databasebeta

← #11806904

Subgroups — #11806904

Order 1152.

1793 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×Dic3×#67C212yesmaximal, complemented
4C2×#63898C211yesmaximal, characteristic, complemented
5#10592920C211yesmaximal, characteristic, complemented
6#10591721C212yesmaximal, complemented
7#10591710C212yesmaximal, complemented
8#10591707C212yesmaximal, complemented
9C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10#10591318C211yesmaximal, characteristic, complemented
11Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#83173—31nomaximal
13#82343—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×#67C2212yes—
17C23×C3×Dic3C2212yes—
18C22×C3×D12C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×#3757C2212yes—
21C2×#3757C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2212yes—
25C3×#940C418yescomplemented
26C3×D4×Dic3—24no—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30Dic3×#67—28no—
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×Dic32C2212yes—
37#63898—24no—
38#63579C2212yes—
39#63579C2211yescharacteristic
40#63579C2211yescharacteristic
41C2×C3×#127—31no—
42C2×C3×C4×D4—31no—
43C2×#940D311yescharacteristic
44C2×D4×Dic3—32no—
45C2×D4×Dic3—31no—
46C2×D4×Dic3D311yescharacteristic, complemented
47C2×C4×#67—32no—
48C2×#893—31no—
49#5221—31no—
50#5221—31no—
51#5221—32no—
52#5221—31no—
53#5221—61no—
54#5220—32no—
55#5220—32no—
56#5213—32no—
57Dic3×C4⋊C4—31no—
58#4957—32no—
59#4956—32no—
60#4939—31no—
61C4×C4⋊Dic3—31no—
62C4×C4⋊Dic3—31no—
63C4×Dic3⋊C4—31no—
64C24×C32C2312yes—
65C23×C3×D3C2312yes—
66C2×C32×D4—22no—
67C2×C32×D4—22no—
68C2×C32×D4C2×C414yescomplemented
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2312yes—
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C3×#67—24no—
74C2×C3×#67—24no—
75C2×C3×#67—42no—
76C2×C3×#67—42no—
77C2×C3×#67C2×C418yescomplemented
78C2×C3×#67C2×C418yescomplemented
79C22×C3×Dic3—24no—
80C22×C3×Dic3—24no—
81C22×C3×Dic3—42no—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×D12—22no—
88C2×C3×D12—22no—
89C2×C3×D12C2×C414yescomplemented
90C2×D3×Dic3—24no—
91C2×D3×Dic3—24no—
92C2×D3×Dic3—42no—
93#3757—24no—
94#3757—42no—
95C4⋊(C3⋊Dic3)—22no—
96C4×C3⋊Dic3—22no—
97C3×#217—24no—
98C3×C4⋊Dic3D414yescomplemented
99C3×C4×Dic3—22no—
100C3×C4×Dic3C2×C414yescomplemented
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3D414yescomplemented
103(C2×D3)⋊Dic3—24no—
104(C2×D3)⋊Dic3—24no—
105(C2×D3)⋊Dic3—42no—
106Dic32—24no—
107#2366—91noSylow
108C22×C3×D4—21no—
109C22×C3×D4—32no—
110C22×C3×D4—32no—
111C22×C3×D4—31no—
112C22×C3×D4C2×D311yescharacteristic
113C22×C3×D4C2×D311yescharacteristic
114C23×C3×C4—32no—
115C22×#67C2×D312yes—
116C22×#67C2×D312yes—
117C23×Dic3—32no—
118C23×Dic3C2×D312yes—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—32no—
121C3×#127—38no—
122C3×C4×D4—64no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C42—31no—
126C2×C3×C42—31no—
127C2×#217—32no—
128C2×#217—32no—
129C2×#217—32no—
130C2×#217—32no—
131C2×#217—32no—
132C2×#217—32no—
133C2×#217—32no—
134C2×#217—62no—
135C2×#217—62no—
136C2×#217C2×D312yes—
137#940Dic318yescomplemented
138D4×Dic3—24no—
139D4×Dic3—68no—
140D4×Dic3—64no—
141C4×#67—68no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—61no—
150C2×C4⋊Dic3C2×D311yescharacteristic
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—31no—
155C2×C4×Dic3—32no—
156C2×C4×Dic3—32no—
157C2×C4×Dic3—61no—
158C2×C4×Dic3C2×D311yescharacteristic
159C2×C4×Dic3C2×D311yescharacteristic
160#893—64no—
161C3⋊#95—31no—
162C3⋊#95—31no—
163C3⋊#95—31no—
164C3⋊#95—31no—
165C3⋊#95—32no—
166C3⋊#95—32no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32C22×C414yes—
174C23×C32C2411yescharacteristic
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3C22×C414yes—
182C32×D4—28no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C2×D412yes—
185C2×C32×C4#4112yes—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3C2×D412yes—
195C3×#67—216no—
196C3×#67—48no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—48no—
207C2×C3×Dic3C22×C412yes—
208C2×C3×Dic3C22×C412yes—
209C2×C3×Dic3C2×D412yes—
210C2×C3×Dic3C2×D412yes—
211C2×C3×Dic3C2×D414yes—
212C2×C3×Dic3#4112yes—
213C3×D12—28no—
214D3×Dic3—48no—
215C2×#127—31no—
216C2×C4×D4—31no—
217C2×C4×D4—91no—
218C2×C4×D4—92no—
219#390—91no—
220#390—92no—
221#390—91no—
222#386—92no—
223#386—92no—
224C4×C4⋊C4—91no—
225C4×C4⋊C4—91no—
226C24×C3—22no—
227C24×C3—32no—
228C24×C3C22×D312yes—
229C24×C3C22×D312yes—
230C23×D3C22×D312yes—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4—22no—
234C2×C3×D4—22no—
235C2×C3×D4—24no—
236C2×C3×D4—38no—
237C2×C3×D4—38no—
238C2×C3×D4—34no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—64no—
242C2×C3×D4—64no—
243C2×C3×D4—62no—
244C2×C3×D4—62no—
245C2×C3×D4—122no—
246C2×C3×D4—122no—
247C2×C3×D4C4×D314yescomplemented
248C2×C3×D4C2×Dic314yescomplemented
249C22×C3×C4—21no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—32no—
253C22×C3×C4—31no—
254C22×C3×C4—31no—
255C22×C3×C4—64no—
256C22×C3×C4—64no—
257C22×C3×C4—122no—
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C2×#67—24no—
261C2×#67—24no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67C2×Dic318yescomplemented
265C2×#67C2×Dic318yescomplemented
266C22×Dic3—24no—
267C22×Dic3—24no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—32no—
272C22×Dic3—32no—
273C22×Dic3—31no—
274C22×Dic3—42no—
275C22×Dic3—61no—
276C22×Dic3—61no—
277C22×Dic3—62no—
278C22×Dic3—64no—
279C22×Dic3—64no—
280C22×Dic3—122no—
281C22×Dic3C22×D311yescharacteristic
282C22×Dic3C22×D311yescharacteristic
283C22×Dic3C22×D311yescharacteristic
284C22×Dic3C22×D312yes—
285C22×Dic3C22×D311yescharacteristic
286C2×D12—22no—
287C2×D12—22no—
288C2×D12C2×Dic314yescomplemented
289C2×C4×D3—64no—
290C2×C4×D3—64no—
291C2×C4×D3—122no—
292C3×C4⋊C4—34no—
293C3×C22⋊C4—64no—
294C3×C42—34no—
295C3×C42—62no—
296#217—24no—
297#217—64no—
298#217—64no—
299#217—64no—
300#217—64no—
301#217—124no—
302#217—122no—
303#217—122no—
304#217—122no—
305#217—124no—
306(C2×D3)⋊C4—64no—
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—122no—
309C4⋊Dic3—34no—
310C4⋊Dic3—62no—
311C4⋊Dic3—62no—
312C4⋊Dic3—62no—
313C4⋊Dic3—122no—
314C4⋊Dic3#6714yescomplemented
315Dic3⋊C4—34no—
316Dic3⋊C4—62no—
317C4×Dic3—22no—
318C4×Dic3—64no—
319C4×Dic3—62no—
320C4×Dic3—62no—
321C4×Dic3—64no—
322C4×Dic3—122no—
323C4×Dic3C2×Dic314yescomplemented
324C22×C32—24no—
325C22×C32—24no—
326C22×C32—24no—
327C22×C32—42no—
328C22×C32—42no—
329C22×C32—42no—
330C22×C32—42no—
331C22×C32C23×C411yescharacteristic
332C22×C32C22×D411yescharacteristic
333C22×C32C22×D411yescharacteristic
334C22×C32C2×#4111yescharacteristic
335C22×C32C2×#4111yescharacteristic
336C22×C32H(5,𝔽2)11yescharacteristic
337C22×C32H(5,𝔽2)11yescharacteristic
338C2×C3×D3—24no—
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—42no—
342C2×C3×D3—42no—
343C2×C3×D3—42no—
344C2×C3×D3—42no—
345C32×C4C4×D414yescomplemented
346C3⋊Dic3—22no—
347C3⋊Dic3—41no—
348C3⋊Dic3—42no—
349C3×Dic3—22no—
350C3×Dic3—24no—
351C3×Dic3—22no—
352C3×Dic3—41no—
353C3×Dic3C4×D414yescomplemented
354C22×D4—32no—
355C22×D4—32no—
356C22×D4—31no—
357C22×D4D3211yescharacteristic
358C23×C4—32no—
359C23×C4—92no—
360#127—38no—
361C4×D4—64no—
362C4×D4—184no—
363C4×D4—188no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—91no—
368C2×C22⋊C4—32no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C42—31no—
375C2×C42—31no—
376C2×C42—92no—
377C2×C42—91no—
378#95—91no—
379#95—92no—
380#95—91no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—21no—
394C23×C3—24no—
395C23×C3—34no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—62no—
403C23×C3—62no—
404C23×C3—62no—
405C23×C3—62no—
406C23×C3—62no—
407C23×C3—62no—
408C23×C3C2×C4×D314yes—
409C23×C3C22×Dic314yes—
410C23×C3C23×D311yescharacteristic
411C23×C3C23×D311yescharacteristic
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3C22×Dic314yes—
419C3×D4—28no—
420C3×D4—28no—
421C3×D4—48no—
422C3×D4—616no—
423C3×D4—68no—
424C3×D4—128no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—32no—
429C2×C3×C4—32no—
430C2×C3×C4—32no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—34no—
434C2×C3×C4—62no—
435C2×C3×C4—61no—
436C2×C3×C4—62no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—61no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—128no—
444C2×C3×C4C2×C4×D312yes—
445C2×C3×C4#23512yes—
446C2×C3×C4D3×D412yes—
447C2×C3×C4#23712yes—
448C2×C3×C4C22×Dic312yes—
449C2×C3×C4C2×#6712yes—
450#67—216no—
451#67—48no—
452C2×Dic3—22no—
453C2×Dic3—21no—
454C2×Dic3—22no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—32no—
462C2×Dic3—32no—
463C2×Dic3—48no—
464C2×Dic3—62no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—61no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—61no—
475C2×Dic3—62no—
476C2×Dic3—62no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—62no—
481C2×Dic3—61no—
482C2×Dic3—121no—
483C2×Dic3—121no—
484C2×Dic3—121no—
485C2×Dic3—121no—
486C2×Dic3—122no—
487C2×Dic3—122no—
488C2×Dic3—122no—
489C2×Dic3—128no—
490C2×Dic3D3×D412yes—
491C2×Dic3D3×D412yes—
492C2×Dic3#23712yes—
493C2×Dic3C22×Dic312yes—
494C2×Dic3C22×Dic312yes—
495C2×Dic3C2×#6714yes—
496D12—28no—
497C4×D3—128no—
498C2×C32—44no—
499C2×C32C2×C4×D411yescharacteristic
500C2×C32C2×C4×D411yescharacteristic
501C2×C32#51811yescharacteristic
502C2×C32D4211yescharacteristic
503C2×C32#55011yescharacteristic
504C2×C32#55011yescharacteristic
505C2×C32#55911yescharacteristic
506C3×D3—44no—
507C24—32no—
508C24C2×D3212yes—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—38no—
512C2×D4—38no—
513C2×D4—34no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—62no—
517C2×D4—62no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4D3×Dic314yescomplemented
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—32no—
525C22×C4—31no—
526C22×C4—64no—
527C22×C4—64no—
528C22×C4—91no—
529C22×C4—92no—
530C22×C4—91no—
531C22×C4—122no—
532C22×C4—184no—
533C22×C4—184no—
534C22×C4—362no—
535C22×C4C2×D3211yescharacteristic
536C4⋊C4—34no—
537C4⋊C4—94no—
538C4⋊C4—182no—
539C4⋊C4—182no—
540C22⋊C4—64no—
541C22⋊C4—184no—
542C22⋊C4—184no—
543C22⋊C4—184no—
544C22⋊C4—362no—
545C22⋊C4—362no—
546C42—34no—
547C42—62no—
548C42—184no—
549C42—182no—
550C22×C3—24no—
551C22×C3—24no—
552C22×C3—24no—
553C22×C3—24no—
554C22×C3—24no—
555C22×C3—24no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—44no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—42no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—64no—
575C22×C3—64no—
576C22×C3—64no—
577C22×C3—82no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—122no—
582C22×C3—122no—
583C22×C3—122no—
584C22×C3—122no—
585C22×C3C22×C4×D311yescharacteristic
586C22×C3C2×#23511yescharacteristic
587C22×C3C2×D3×D411yescharacteristic
588C22×C3C2×D3×D411yescharacteristic
589C22×C3C2×D3×D411yescharacteristic
590C22×C3C2×#23711yescharacteristic
591C22×C3C2×#23711yescharacteristic
592C22×C3#100411yescharacteristic
593C22×C3#100411yescharacteristic
594C22×C3#100411yescharacteristic
595C22×C3D3×#4111yescharacteristic
596C22×C3#100911yescharacteristic
597C22×C3C23×Dic311yescharacteristic
598C22×C3C22×#6711yescharacteristic
599C2×D3—24no—
600C2×D3—24no—
601C2×D3—24no—
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C3×C4—24no—
607C3×C4—34no—
608C3×C4—64no—
609C3×C4—62no—
610C3×C4—62no—
611C3×C4—121no—
612C3×C4C4×#6714yescomplemented
613C3×C4D4×Dic314yescomplemented
614Dic3—22no—
615Dic3—22no—
616Dic3—24no—
617Dic3—41no—
618Dic3—62no—
619Dic3—62no—
620Dic3—122no—
621Dic3—122no—
622Dic3—122no—
623Dic3—121no—
624Dic3—122no—
625Dic3—121no—
626Dic3—242no—
627Dic3D4×Dic314yescomplemented
628C32#236611yescharacteristic, complemented, Sylow
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—34no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23C2×D3×Dic314yes—
643C23C22×D3211yescharacteristic
644D4—28no—
645D4—616no—
646D4—68no—
647D4—128no—
648C2×C4—32no—
649C2×C4—32no—
650C2×C4—32no—
651C2×C4—32no—
652C2×C4—32no—
653C2×C4—34no—
654C2×C4—62no—
655C2×C4—61no—
656C2×C4—62no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—92no—
664C2×C4—128no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—182no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—182no—
671C2×C4—182no—
672C2×C4—181no—
673C2×C4—368no—
674C2×C4C2×D3×Dic312yes—
675C2×C4#380412yes—
676C2×C4D3×#6712yes—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—44no—
685C2×C3—44no—
686C2×C3—84no—
687C2×C3—124no—
688C2×C3C4×D3×D411yescharacteristic
689C2×C3#554511yescharacteristic
690C2×C3#555311yescharacteristic
691C2×C3#555911yescharacteristic
692C2×C3#571311yescharacteristic
693C2×C3#571711yescharacteristic
694C2×C3#571811yescharacteristic
695C2×C3#571811yescharacteristic
696C2×C3C2×C4×#6711yescharacteristic
697C2×C3C2×D4×Dic311yescharacteristic
698C2×C3C2×D4×Dic311yescharacteristic
699C2×C3#579811yescharacteristic
700C2×C3D4×#6711yescharacteristic
701C2×C3#583411yescharacteristic
702D3—44no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—64no—
711C22—64no—
712C22—64no—
713C22—122no—
714C22—122no—
715C22—122no—
716C22—122no—
717C22D32×D411yescharacteristic
718C22D3×#23711yescharacteristic
719C22#6431311yescharacteristic
720C22#6431411yescharacteristic
721C22C22×D3×Dic311yescharacteristic
722C22C2×#380411yescharacteristic
723C22C2×D3×#6711yescharacteristic
724C4—34no—
725C4—62no—
726C4—62no—
727C4—64no—
728C4—121no—
729C4—182no—
730C4—362no—
731C4—361no—
732C4Dic3×#6714yescomplemented
733C3—21no—
734C3#8234311yescharacteristic, complemented
735C3#8317311yescharacteristic, complemented
736C2—44no—
737C2—124no—
738C2D3×D4×Dic311yescharacteristic
739C2#1059514311yescharacteristic
740C2#1059515811yescharacteristic
741C2#1059519811yescharacteristic
742C2#1059521511yescharacteristic
743C2#1059529311yescharacteristic
744C2C2×Dic3×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32#2366
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic3C2semidirect
3. C2×Dic3×#67C2semidirect
4. C2×#63898C2semidirect
5. #10592920C2semidirect
6. #10591721C2semidirect
7. #10591710C2semidirect
8. #10591707C2semidirect
9. C4×Dic3⋊Dic3C2semidirect
10. #10591318C2semidirect
11. Dic3×C4⋊Dic3C2semidirect
25. C3×#940C4semidirect
46. C2×D4×Dic3D3semidirect
68. C2×C32×D4C2×C4semidirect
77. C2×C3×#67C2×C4semidirect
78. C2×C3×#67C2×C4semidirect
89. C2×C3×D12C2×C4semidirect
98. C3×C4⋊Dic3D4semidirect
100. C3×C4×Dic3C2×C4semidirect
102. Dic3⋊Dic3D4semidirect
137. #940Dic3semidirect
247. C2×C3×D4C4×D3semidirect
248. C2×C3×D4C2×Dic3semidirect
264. C2×#67C2×Dic3semidirect
265. C2×#67C2×Dic3semidirect
288. C2×D12C2×Dic3semidirect
314. C4⋊Dic3#67semidirect
323. C4×Dic3C2×Dic3semidirect
345. C32×C4C4×D4semidirect
353. C3×Dic3C4×D4semidirect
520. C2×D4D3×Dic3semidirect
612. C3×C4C4×#67semidirect
613. C3×C4D4×Dic3semidirect
627. Dic3D4×Dic3semidirect
628. C32#2366semidirect
732. C4Dic3×#67semidirect
734. C3#82343semidirect
735. C3#83173semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×C3×D4×Dic32
C2×Dic3×#672
C2×#638982
#105929202
#105917212
#105917102
#105917072
C4×Dic3⋊Dic32
#105913182
Dic3×C4⋊Dic32
#831733
#823433