Finite Group Databasebeta

← #11806906

Subgroups — #11806906

Order 1152.

1877 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic
3C2×#67⋊Dic3C212yesmaximal, complemented
4C2×Dic3×D12C211yesmaximal, characteristic, complemented
5C3×#5221C211yesmaximal, characteristic, complemented
6#10591721C212yesmaximal, complemented
7#10591713C212yesmaximal, complemented
8#10591707C212yesmaximal, complemented
9C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10#10591323C211yesmaximal, characteristic, complemented
11Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#83173—31nomaximal
13#76306—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3C2212yes—
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×D12C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×#3757C2212yes—
21D4×C3⋊Dic3—24no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C3×#940C418yescomplemented
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30#67⋊Dic3—28no—
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×Dic32C2212yes—
37Dic3×D12—24no—
38#63579C2212yes—
39#63579C2211yescharacteristic
40#63579C2211yescharacteristic
41C2×C3×#127—31no—
42C2×#940D311yescharacteristic
43C2×D4×Dic3—31no—
44C2×D4×Dic3—31no—
45C2×D4×Dic3—32no—
46C2×D4×Dic3—31no—
47C2×D4×Dic3—61no—
48C2×#67⋊C4—32no—
49C2×C4×D12—31no—
50C3×#390—31no—
51#5221—32no—
52#5221—31no—
53#5221D311yescharacteristic, complemented
54#5220—32no—
55#5220—32no—
56#4988—31no—
57Dic3×C4⋊C4—31no—
58#4958—32no—
59#4957—32no—
60#4956—32no—
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⋊Dic3—24no—
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3—42no—
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2312yes—
75C22×C3⋊Dic3C2311yescharacteristic
76C2×C3×#67—24no—
77C2×C3×#67—24no—
78C2×C3×#67—42no—
79C2×C3×#67—42no—
80C2×C3×#67C2×C418yescomplemented
81C2×C3×#67C2×C418yescomplemented
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
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—
94C4⋊(C3⋊Dic3)D414yescomplemented
95C4×C3⋊Dic3—22no—
96C3×#217—24no—
97C3×#217—42no—
98C3×C4⋊Dic3—22no—
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
114C22×#67C2×D312yes—
115C22×#67C2×D312yes—
116C23×Dic3—32no—
117C23×Dic3—32no—
118C23×Dic3—32no—
119C23×Dic3—62no—
120C22×D12C2×D311yescharacteristic
121C22×C4×D3—32no—
122C3×#127—38no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—32no—
126C2×C3×C42—31no—
127C2×C3×C42—31no—
128C2×#217—32no—
129C2×#217—32no—
130C2×#217—32no—
131C2×#217—32no—
132C2×#217—32no—
133C2×#217—62no—
134C2×#217C2×D312yes—
135C2×#217C2×D312yes—
136#940Dic318yescomplemented
137D4×Dic3—64no—
138D4×Dic3—68no—
139D4×Dic3—64no—
140D4×Dic3—64no—
141D4×Dic3—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#67⋊C4—68no—
161C4×D12—64no—
162C3⋊#95—31no—
163C3⋊#95—31no—
164C3⋊#95—32no—
165C3⋊#95—31no—
166C3⋊#95—31no—
167C3⋊#95—32no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32—22no—
174C23×C32C22×C414yes—
175C23×C32C2411yescharacteristic
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3C22×C414yes—
183C32×D4—28no—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C2×D412yes—
186C2×C32×C4#4112yes—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—48no—
195C2×C3⋊Dic3C2×D412yes—
196C2×C3⋊Dic3C2×D414yes—
197C3×#67—216no—
198C3×#67—48no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3C22×C412yes—
210C2×C3×Dic3C22×C412yes—
211C2×C3×Dic3C2×D412yes—
212C2×C3×Dic3C2×D412yes—
213C2×C3×Dic3#4112yes—
214C3×D12—28no—
215D3×Dic3—48no—
216C2×#127—31no—
217C2×C4×D4—91no—
218C2×C4×D4—92no—
219C2×C4×D4—91no—
220#390—31no—
221#390—92no—
222#390—91no—
223#386—92no—
224#386—92no—
225C4×C4⋊C4—91no—
226C4×C4⋊C4—91no—
227C24×C3—22no—
228C24×C3—32no—
229C24×C3C22×D312yes—
230C24×C3C22×D312yes—
231C23×D3C22×D312yes—
232C2×C3×D4—24no—
233C2×C3×D4—24no—
234C2×C3×D4—22no—
235C2×C3×D4—22no—
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4—24no—
239C2×C3×D4—38no—
240C2×C3×D4—38no—
241C2×C3×D4—34no—
242C2×C3×D4—64no—
243C2×C3×D4—64no—
244C2×C3×D4—62no—
245C2×C3×D4—62no—
246C2×C3×D4—122no—
247C2×C3×D4—122no—
248C2×C3×D4C4×D314yescomplemented
249C2×C3×D4C2×Dic314yescomplemented
250C22×C3×C4—21no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—32no—
255C22×C3×C4—31no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—24no—
259C2×#67—24no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67C2×Dic318yescomplemented
263C2×#67C2×Dic318yescomplemented
264C22×Dic3—31no—
265C22×Dic3—32no—
266C22×Dic3—31no—
267C22×Dic3—32no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—61no—
271C22×Dic3—61no—
272C22×Dic3—62no—
273C22×Dic3—64no—
274C22×Dic3—64no—
275C22×Dic3—64no—
276C22×Dic3—64no—
277C22×Dic3—64no—
278C22×Dic3—68no—
279C22×Dic3—64no—
280C22×Dic3—124no—
281C22×Dic3—122no—
282C22×Dic3—122no—
283C22×Dic3—122no—
284C22×Dic3—124no—
285C22×Dic3C22×D312yes—
286C22×Dic3C22×D311yescharacteristic
287C22×Dic3C22×D311yescharacteristic
288C22×Dic3C22×D311yescharacteristic
289C22×Dic3C22×D311yescharacteristic
290C2×D12—22no—
291C2×D12—22no—
292C2×D12C2×Dic314yescomplemented
293C2×C4×D3—64no—
294C2×C4×D3—64no—
295C2×C4×D3—122no—
296C3×C4⋊C4—62no—
297C3×C22⋊C4—64no—
298C3×C22⋊C4—122no—
299C3×C42—34no—
300C3×C42—62no—
301#217—24no—
302#217—42no—
303#217—64no—
304#217—64no—
305#217—64no—
306#217—64no—
307#217—68no—
308#217—122no—
309(C2×D3)⋊C4—64no—
310(C2×D3)⋊C4—64no—
311(C2×D3)⋊C4—122no—
312C4⋊Dic3—22no—
313C4⋊Dic3—34no—
314C4⋊Dic3—34no—
315C4⋊Dic3—34no—
316C4⋊Dic3—64no—
317C4⋊Dic3—62no—
318Dic3⋊C4—34no—
319Dic3⋊C4—62no—
320C4×Dic3—22no—
321C4×Dic3—64no—
322C4×Dic3—64no—
323C4×Dic3—62no—
324C4×Dic3—62no—
325C4×Dic3—64no—
326C4×Dic3C2×Dic314yescomplemented
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—24no—
330C22×C32—42no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32—42no—
334C22×C32C23×C411yescharacteristic
335C22×C32C22×D411yescharacteristic
336C22×C32C22×D411yescharacteristic
337C22×C32C2×#4111yescharacteristic
338C22×C32C2×#4111yescharacteristic
339C22×C32H(5,𝔽2)11yescharacteristic
340C22×C32H(5,𝔽2)11yescharacteristic
341C2×C3×D3—24no—
342C2×C3×D3—24no—
343C2×C3×D3—24no—
344C2×C3×D3—42no—
345C2×C3×D3—42no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348C32×C4C4×D414yescomplemented
349C3⋊Dic3—22no—
350C3⋊Dic3—24no—
351C3⋊Dic3—41no—
352C3×Dic3—22no—
353C3×Dic3—22no—
354C3×Dic3—42no—
355C3×Dic3—41no—
356C3×Dic3C4×D414yescomplemented
357C22×D4—32no—
358C22×D4—32no—
359C22×D4—31no—
360C22×D4D3211yescharacteristic
361C23×C4—92no—
362C23×C4—92no—
363#127—38no—
364C4×D4—184no—
365C4×D4—188no—
366C4×D4—184no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4—91no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C42—31no—
378C2×C42—31no—
379C2×C42—92no—
380C2×C42—91no—
381#95—91no—
382#95—91no—
383#95—92no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—21no—
399C23×C3—24no—
400C23×C3—34no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—62no—
406C23×C3—62no—
407C23×C3—62no—
408C23×C3—62no—
409C23×C3—62no—
410C23×C3—62no—
411C23×C3C2×C4×D314yes—
412C23×C3C22×Dic314yes—
413C23×C3C23×D311yescharacteristic
414C23×C3C23×D311yescharacteristic
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3C22×Dic314yes—
422C3×D4—216no—
423C3×D4—28no—
424C3×D4—28no—
425C3×D4—616no—
426C3×D4—68no—
427C3×D4—128no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—61no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—61no—
440C2×C3×C4—62no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—62no—
444C2×C3×C4—62no—
445C2×C3×C4—61no—
446C2×C3×C4C2×C4×D312yes—
447C2×C3×C4D3×D412yes—
448C2×C3×C4D3×D412yes—
449C2×C3×C4#23712yes—
450C2×C3×C4#23712yes—
451C2×C3×C4C22×Dic312yes—
452#67—216no—
453#67—48no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—21no—
462C2×Dic3—22no—
463C2×Dic3—21no—
464C2×Dic3—32no—
465C2×Dic3—34no—
466C2×Dic3—32no—
467C2×Dic3—34no—
468C2×Dic3—62no—
469C2×Dic3—64no—
470C2×Dic3—62no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—62no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—62no—
480C2×Dic3—62no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—121no—
488C2×Dic3—121no—
489C2×Dic3—122no—
490C2×Dic3—122no—
491C2×Dic3—128no—
492C2×Dic3—128no—
493C2×Dic3—128no—
494C2×Dic3—1216no—
495C2×Dic3D3×D412yes—
496C2×Dic3D3×D412yes—
497C2×Dic3#23712yes—
498C2×Dic3C22×Dic312yes—
499C2×Dic3C22×Dic312yes—
500D12—28no—
501C4×D3—128no—
502C2×C32—44no—
503C2×C32C2×C4×D411yescharacteristic
504C2×C32C2×C4×D411yescharacteristic
505C2×C32#51811yescharacteristic
506C2×C32D4211yescharacteristic
507C2×C32#55011yescharacteristic
508C2×C32#55011yescharacteristic
509C2×C32#55911yescharacteristic
510C3×D3—44no—
511C24—32no—
512C24C2×D3212yes—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—38no—
516C2×D4—38no—
517C2×D4—34no—
518C2×D4—64no—
519C2×D4—64no—
520C2×D4—62no—
521C2×D4—62no—
522C2×D4—122no—
523C2×D4—122no—
524C2×D4D3×Dic314yescomplemented
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—32no—
530C22×C4—91no—
531C22×C4—92no—
532C22×C4—91no—
533C22×C4—184no—
534C22×C4—184no—
535C22×C4—184no—
536C22×C4—184no—
537C22×C4—362no—
538C22×C4—362no—
539C22×C4C2×D3211yescharacteristic
540C4⋊C4—62no—
541C4⋊C4—94no—
542C4⋊C4—94no—
543C4⋊C4—182no—
544C22⋊C4—64no—
545C22⋊C4—122no—
546C22⋊C4—184no—
547C22⋊C4—184no—
548C22⋊C4—184no—
549C22⋊C4—362no—
550C42—34no—
551C42—62no—
552C42—184no—
553C42—182no—
554C22×C3—28no—
555C22×C3—24no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—24no—
559C22×C3—24no—
560C22×C3—24no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—64no—
583C22×C3—64no—
584C22×C3—64no—
585C22×C3—122no—
586C22×C3—122no—
587C22×C3—122no—
588C22×C3—122no—
589C22×C3C22×C4×D311yescharacteristic
590C22×C3C2×D3×D411yescharacteristic
591C22×C3C2×D3×D411yescharacteristic
592C22×C3C2×D3×D411yescharacteristic
593C22×C3C2×D3×D411yescharacteristic
594C22×C3C2×#23711yescharacteristic
595C22×C3C2×#23711yescharacteristic
596C22×C3C2×#23711yescharacteristic
597C22×C3#100411yescharacteristic
598C22×C3#100411yescharacteristic
599C22×C3#100411yescharacteristic
600C22×C3D3×#4111yescharacteristic
601C22×C3#100911yescharacteristic
602C22×C3C23×Dic311yescharacteristic
603C2×D3—24no—
604C2×D3—24no—
605C2×D3—24no—
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—42no—
609C2×D3—42no—
610C3×C4—24no—
611C3×C4—34no—
612C3×C4—62no—
613C3×C4—62no—
614C3×C4—122no—
615C3×C4—121no—
616C3×C4#67⋊C414yescomplemented
617C3×C4D4×Dic314yescomplemented
618Dic3—22no—
619Dic3—22no—
620Dic3—42no—
621Dic3—41no—
622Dic3—64no—
623Dic3—64no—
624Dic3—62no—
625Dic3—62no—
626Dic3—64no—
627Dic3—124no—
628Dic3—122no—
629Dic3—121no—
630Dic3—121no—
631Dic3D4×Dic314yescomplemented
632C32#236611yescharacteristic, complemented, Sylow
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—34no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—62no—
646C23C2×D3×Dic314yes—
647C23C22×D3211yescharacteristic
648D4—28no—
649D4—616no—
650D4—68no—
651D4—128no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—62no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—61no—
667C2×C4—92no—
668C2×C4—94no—
669C2×C4—182no—
670C2×C4—181no—
671C2×C4—182no—
672C2×C4—181no—
673C2×C4—181no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—368no—
677C2×C4—368no—
678C2×C4C2×D3×Dic312yes—
679C2×C4#380512yes—
680C2×C4#381112yes—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—48no—
689C2×C3—44no—
690C2×C3—44no—
691C2×C3—124no—
692C2×C3C2×#67⋊C411yescharacteristic
693C2×C3C4×D3×D411yescharacteristic
694C2×C3#554511yescharacteristic
695C2×C3#559911yescharacteristic
696C2×C3#560911yescharacteristic
697C2×C3#568111yescharacteristic
698C2×C3#571311yescharacteristic
699C2×C3#571711yescharacteristic
700C2×C3#571811yescharacteristic
701C2×C3#571811yescharacteristic
702C2×C3#571811yescharacteristic
703C2×C3C2×D4×Dic311yescharacteristic
704C2×C3C2×D4×Dic311yescharacteristic
705C2×C3#579811yescharacteristic
706D3—44no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—64no—
715C22—64no—
716C22—64no—
717C22—122no—
718C22—122no—
719C22—122no—
720C22—122no—
721C22D32×D411yescharacteristic
722C22D3×#23711yescharacteristic
723C22#6431311yescharacteristic
724C22#6431411yescharacteristic
725C22C22×D3×Dic311yescharacteristic
726C22C2×#380511yescharacteristic
727C22C2×#381111yescharacteristic
728C4—34no—
729C4—62no—
730C4—62no—
731C4—122no—
732C4—121no—
733C4—182no—
734C4—184no—
735C4—361no—
736C4#67⋊Dic314yescomplemented
737C3—21no—
738C3#7630611yescharacteristic, complemented
739C3#8317311yescharacteristic, complemented
740C2—44no—
741C2—124no—
742C2D3×D4×Dic311yescharacteristic
743C2#1059514411yescharacteristic
744C2#1059516411yescharacteristic
745C2#1059519911yescharacteristic
746C2#1059521511yescharacteristic
747C2#1059529711yescharacteristic
748C2C2×#67⋊Dic311yescharacteristic
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
1. C2×D4×C3⋊Dic3C2semidirect
3. C2×#67⋊Dic3C2semidirect
4. C2×Dic3×D12C2semidirect
5. C3×#5221C2semidirect
6. #10591721C2semidirect
7. #10591713C2semidirect
8. #10591707C2semidirect
9. C4×Dic3⋊Dic3C2semidirect
10. #10591323C2semidirect
11. Dic3×C4⋊Dic3C2semidirect
26. C3×#940C4semidirect
53. #5221D3semidirect
68. C2×C32×D4C2×C4semidirect
80. C2×C3×#67C2×C4semidirect
81. C2×C3×#67C2×C4semidirect
89. C2×C3×D12C2×C4semidirect
94. C4⋊(C3⋊Dic3)D4semidirect
100. C3×C4×Dic3C2×C4semidirect
102. Dic3⋊Dic3D4semidirect
136. #940Dic3semidirect
248. C2×C3×D4C4×D3semidirect
249. C2×C3×D4C2×Dic3semidirect
262. C2×#67C2×Dic3semidirect
263. C2×#67C2×Dic3semidirect
292. C2×D12C2×Dic3semidirect
326. C4×Dic3C2×Dic3semidirect
348. C32×C4C4×D4semidirect
356. C3×Dic3C4×D4semidirect
524. C2×D4D3×Dic3semidirect
616. C3×C4#67⋊C4semidirect
617. C3×C4D4×Dic3semidirect
631. Dic3D4×Dic3semidirect
632. C32#2366semidirect
736. C4#67⋊Dic3semidirect
738. C3#76306semidirect
739. C3#83173semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9402
C2×#67⋊Dic32
C2×Dic3×D122
C3×#52212
#105917212
#105917132
#105917072
C4×Dic3⋊Dic32
#105913232
Dic3×C4⋊Dic32
#831733
#763063