Finite Group Databasebeta

← #11801997

Subgroups — #11801997

Order 1152.

2661 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
1C23×D3×Dic3C211yesmaximal, characteristic, complemented
2C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic
4C2×#67⋊Dic3C212yesmaximal, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6#10591721C212yesmaximal, complemented
7#10591718C211yesmaximal, characteristic, complemented
8#10591706C211yesmaximal, characteristic, complemented
9#10591705C211yesmaximal, characteristic, complemented
10#10591379C212yesmaximal, complemented
11#10591368C212yesmaximal, complemented
12Dic3×#120—31nomaximal
13#74659—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C23×C3⋊Dic3C2211yescharacteristic, complemented
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2211yescharacteristic
20C22×D3×Dic3—24no—
21C22×D3×Dic3—28no—
22C22×D3×Dic3C2212yes—
23C22×D3×Dic3C2212yes—
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic, complemented
26D4×C3⋊Dic3—24no—
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
28C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2212yescomplemented
32C3×#937C418yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34#67⋊Dic3—28no—
35C2×Dic3⋊Dic3C2212yescomplemented
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2212yescomplemented
39C3×C3⋊#95C2212yescomplemented
40#63579C2212yescomplemented
41#63579C2212yescomplemented
42C24×Dic3—31no—
43C23×C4×D3—31no—
44C2×C3×#120—31no—
45C2×#937D311yescharacteristic
46C2×D4×Dic3—31no—
47C2×D4×Dic3—31no—
48C2×D4×Dic3—32no—
49C2×D4×Dic3—61no—
50C2×#67⋊C4—32no—
51C3×#386—31no—
52#5247—31no—
53#5220—32no—
54#5220D311yescharacteristic, complemented
55#5210—31no—
56#4956—32no—
57#4955—31no—
58#4950—31no—
59#4950—32no—
60Dic3×C22⋊C4—31no—
61Dic3×C22⋊C4—31no—
62Dic3×C22⋊C4—32no—
63#4668—32no—
64#4666—32no—
65C24×C32C2311yescharacteristic
66C24×C32C2311yescharacteristic
67C23×C3×D3—22no—
68C23×C3×D3—22no—
69C23×C3×D3—24no—
70C23×C3×D3—24no—
71C23×C3×D3C2×C414yescomplemented
72C23×C3×D3C2312yes—
73C2×C32×D4—22no—
74C2×C32×D4—22no—
75C2×C32×D4C2×C414yescomplemented
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3—24no—
78C22×C3⋊Dic3—22no—
79C22×C3⋊Dic3—24no—
80C22×C3⋊Dic3D414yescomplemented
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C2×C3×#67—24no—
86C2×C3×#67—24no—
87C2×C3×#67C2×C418yescomplemented
88C22×C3×Dic3—22no—
89C22×C3×Dic3—24no—
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2312yes—
93C2×D3×Dic3—232no—
94C2×D3×Dic3—24no—
95C2×D3×Dic3—24no—
96C2×D3×Dic3—24no—
97C2×D3×Dic3—24no—
98C2×D3×Dic3—24no—
99C2×D3×Dic3D418yescomplemented
100#3757—22no—
101#3757—22no—
102C4⋊(C3⋊Dic3)—22no—
103C4×C3⋊Dic3—22no—
104C3×#217—22no—
105C3×#217—24no—
106C3×#217C2×C414yescomplemented
107C3×(C2×D3)⋊C4C2×C418yescomplemented
108Dic3⋊Dic3—24no—
109(C2×D3)⋊Dic3—24no—
110(C2×D3)⋊Dic3—24no—
111Dic32—24no—
112C4×#120—91noSylow
113C25×C3—31no—
114C24×D3C2×D311yescharacteristic
115C22×C3×D4—21no—
116C22×C3×D4—32no—
117C22×C3×D4C2×D311yescharacteristic
118C22×C3×D4C2×D311yescharacteristic
119C23×C3×C4—31no—
120C22×#67C2×D312yes—
121C23×Dic3—31no—
122C23×Dic3—31no—
123C23×Dic3—32no—
124C23×Dic3—31no—
125C23×Dic3—31no—
126C23×Dic3—32no—
127C23×Dic3—61no—
128C23×Dic3—61no—
129C23×Dic3—64no—
130C23×Dic3—68no—
131C23×Dic3C2×D311yescharacteristic
132C22×C4×D3—32no—
133C22×C4×D3—32no—
134C22×C4×D3—68no—
135C22×C4×D3—64no—
136C3×#120—38no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—32no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—32no—
141C2×#217—31no—
142C2×#217—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×#217—32no—
146C2×#217—32no—
147C2×#217—61no—
148C2×#217—61no—
149C2×#217C2×D311yescharacteristic
150C2×#217C2×D311yescharacteristic
151C2×#217C2×D312yescomplemented
152#937Dic318yescomplemented
153D4×Dic3—68no—
154D4×Dic3—64no—
155D4×Dic3—64no—
156D4×Dic3—68no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4C2×D312yes—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—32no—
163C2×C4⋊Dic3—61no—
164C2×Dic3⋊C4—32no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—61no—
170#67⋊C4—68no—
171C3×#95—32no—
172C3⋊#95—32no—
173C3⋊#95—32no—
174C3⋊#95—32no—
175C3⋊#95—32no—
176C3⋊#95C2×D312yescomplemented
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—22no—
180C23×C32—22no—
181C23×C32—22no—
182C23×C32—22no—
183C23×C32C22×C412yes—
184C23×C32C22×C412yescomplemented
185C23×C32C2×D412yes—
186C23×C32#4112yes—
187C23×C32C2411yescharacteristic
188C22×C3×D3—216no—
189C22×C3×D3—28no—
190C22×C3×D3—28no—
191C22×C3×D3—28no—
192C22×C3×D3—22no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3—216no—
197C22×C3×D3C22×C414yes—
198C22×C3×D3C2×D414yes—
199C22×C3×D3#4114yes—
200C32×D4—28no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4C22×C412yescomplemented
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—22no—
207C2×C3⋊Dic3—28no—
208C2×C3⋊Dic3—22no—
209C2×C3⋊Dic3—22no—
210C2×C3⋊Dic3—44no—
211C2×C3⋊Dic3C2×D412yes—
212C2×C3⋊Dic3C2×D414yes—
213C2×C3⋊Dic3C2×D412yes—
214C3×#67—216no—
215C2×C3×Dic3—28no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3C22×C414yescomplemented
224C2×C3×Dic3C2×D414yes—
225D3×Dic3—216no—
226D3×Dic3—216no—
227C24×C4—91no—
228C2×#120—31no—
229C2×C4×D4—92no—
230C2×C4×D4—91no—
231#386—31no—
232#386—92no—
233#385—92no—
234#385—91no—
235#379—91no—
236C4×C22⋊C4—92no—
237C4×C22⋊C4—91no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—32no—
241C24×C3—34no—
242C24×C3—64no—
243C24×C3—64no—
244C24×C3—62no—
245C24×C3—62no—
246C24×C3C22×D311yescharacteristic
247C24×C3C22×D311yescharacteristic
248C24×C3C22×D311yescharacteristic
249C24×C3C22×D311yescharacteristic
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—24no—
253C23×D3—24no—
254C23×D3C2×Dic314yescomplemented
255C23×D3C22×D312yes—
256C2×C3×D4—24no—
257C2×C3×D4—24no—
258C2×C3×D4—22no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—22no—
262C2×C3×D4—24no—
263C2×C3×D4—38no—
264C2×C3×D4—64no—
265C2×C3×D4—64no—
266C2×C3×D4C4×D314yescomplemented
267C2×C3×D4C2×Dic314yescomplemented
268C22×C3×C4—21no—
269C22×C3×C4—32no—
270C22×C3×C4—32no—
271C22×C3×C4—32no—
272C22×C3×C4—64no—
273C22×C3×C4—62no—
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D311yescharacteristic
276C2×#67—24no—
277C2×#67—24no—
278C2×#67C2×Dic318yescomplemented
279C22×Dic3—22no—
280C22×Dic3—24no—
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—34no—
284C22×Dic3—34no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—38no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294C22×Dic3—61no—
295C22×Dic3—61no—
296C22×Dic3—64no—
297C22×Dic3—64no—
298C22×Dic3—64no—
299C22×Dic3—64no—
300C22×Dic3—64no—
301C22×Dic3—632no—
302C22×Dic3—64no—
303C22×Dic3—64no—
304C22×Dic3—64no—
305C22×Dic3—62no—
306C22×Dic3—62no—
307C22×Dic3—64no—
308C22×Dic3—64no—
309C22×Dic3—64no—
310C22×Dic3—124no—
311C22×Dic3—124no—
312C22×Dic3C22×D312yes—
313C22×Dic3C22×D312yes—
314C22×Dic3C22×D312yes—
315C2×C4×D3—38no—
316C2×C4×D3—64no—
317C2×C4×D3—64no—
318C2×C4×D3—64no—
319C2×C4×D3—64no—
320C2×C4×D3—632no—
321C2×C4×D3—64no—
322C3×C22⋊C4—34no—
323C3×C22⋊C4—38no—
324C3×C22⋊C4—64no—
325C3×C22⋊C4—62no—
326#217—22no—
327#217—24no—
328#217—64no—
329#217—64no—
330#217—62no—
331#217—62no—
332#217—64no—
333#217—64no—
334#217—62no—
335#217—62no—
336#217C2×Dic314yescomplemented
337(C2×D3)⋊C4—64no—
338(C2×D3)⋊C4—64no—
339(C2×D3)⋊C4C2×Dic318yescomplemented
340C4⋊Dic3—62no—
341C4⋊Dic3—62no—
342C4⋊Dic3—64no—
343C4⋊Dic3—64no—
344Dic3⋊C4—64no—
345C4×Dic3—64no—
346C4×Dic3—64no—
347C4×Dic3—62no—
348C4×Dic3—62no—
349C4×Dic3—64no—
350C22×C32—22no—
351C22×C32—24no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—24no—
355C22×C32—24no—
356C22×C32—41no—
357C22×C32—41no—
358C22×C32—42no—
359C22×C32C4×D414yescomplemented
360C22×C32C23×C411yescharacteristic
361C22×C32C22×D412yes—
362C22×C32C22×D411yescharacteristic
363C22×C32C2×#4111yescharacteristic
364C22×C32C2×#4112yes—
365C2×C3×D3—232no—
366C2×C3×D3—24no—
367C2×C3×D3—24no—
368C2×C3×D3—24no—
369C2×C3×D3—24no—
370C2×C3×D3—24no—
371C2×C3×D3—24no—
372C2×C3×D3C4×D418yescomplemented
373C32×C4—22no—
374C3⋊Dic3—22no—
375C3⋊Dic3—41no—
376C3⋊Dic3—41no—
377C3⋊Dic3#12014yescomplemented
378C3×Dic3—24no—
379C3×Dic3—24no—
380C3×Dic3—42no—
381C25—31no—
382C22×D4—32no—
383C22×D4D3211yescharacteristic
384C23×C4—31no—
385C23×C4—92no—
386C23×C4—92no—
387C23×C4—91no—
388C23×C4—91no—
389C23×C4—188no—
390C23×C4—184no—
391#120—38no—
392C4×D4—188no—
393C4×D4—184no—
394C2×C4⋊C4—92no—
395C2×C4⋊C4—91no—
396C2×C22⋊C4—31no—
397C2×C22⋊C4—32no—
398C2×C22⋊C4—32no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—92no—
401C2×C22⋊C4—92no—
402C2×C22⋊C4—91no—
403C2×C22⋊C4—91no—
404C2×C42—92no—
405C2×C42—91no—
406#95—32no—
407#95—92no—
408#95—92no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—22no—
423C23×C3—21no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—34no—
429C23×C3—34no—
430C23×C3—34no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—616no—
436C23×C3—68no—
437C23×C3—68no—
438C23×C3—616no—
439C23×C3—68no—
440C23×C3—62no—
441C23×C3—62no—
442C23×C3—62no—
443C23×C3—62no—
444C23×C3C2×C4×D312yes—
445C23×C3C2×C4×D312yescomplemented
446C23×C3D3×D412yes—
447C23×C3D3×D412yes—
448C23×C3#23712yes—
449C23×C3#23712yes—
450C23×C3C22×Dic312yes—
451C23×C3C22×Dic312yescomplemented
452C23×C3C23×D311yescharacteristic
453C23×C3C23×D311yescharacteristic
454C22×D3—28no—
455C22×D3—216no—
456C22×D3—28no—
457C22×D3—28no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—216no—
463C22×D3D3×D414yes—
464C22×D3#23714yes—
465C22×D3C22×Dic314yes—
466C3×D4—216no—
467C3×D4—28no—
468C3×D4—28no—
469C3×D4—616no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—34no—
478C2×C3×C4—34no—
479C2×C3×C4—68no—
480C2×C3×C4—62no—
481C2×C3×C4—62no—
482C2×C3×C4—62no—
483C2×C3×C4—62no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—62no—
487C2×C3×C4C2×C4×D312yescomplemented
488C2×C3×C4C22×Dic312yescomplemented
489#67—216no—
490C2×Dic3—28no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—34no—
499C2×Dic3—32no—
500C2×Dic3—34no—
501C2×Dic3—32no—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—62no—
505C2×Dic3—64no—
506C2×Dic3—62no—
507C2×Dic3—616no—
508C2×Dic3—616no—
509C2×Dic3—68no—
510C2×Dic3—68no—
511C2×Dic3—62no—
512C2×Dic3—62no—
513C2×Dic3—62no—
514C2×Dic3—62no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—62no—
522C2×Dic3—62no—
523C2×Dic3—128no—
524C2×Dic3—122no—
525C2×Dic3—122no—
526C2×Dic3—122no—
527C2×Dic3—124no—
528C2×Dic3—124no—
529C2×Dic3—128no—
530C2×Dic3D3×D414yes—
531C2×Dic3C22×Dic314yescomplemented
532C4×D3—616no—
533C4×D3—616no—
534C2×C32—24no—
535C2×C32—42no—
536C2×C32C2×C4×D411yescharacteristic
537C2×C32C2×C4×D412yes—
538C2×C32C2×#12011yescharacteristic
539C2×C32#52511yescharacteristic
540C2×C32#52512yes—
541C3×D3—28no—
542C24—32no—
543C24—34no—
544C24—64no—
545C24—64no—
546C24—62no—
547C24—62no—
548C24C2×D3211yescharacteristic
549C24C2×D3211yescharacteristic
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—38no—
553C2×D4—64no—
554C2×D4—64no—
555C2×D4D3×Dic314yescomplemented
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—64no—
560C22×C4—62no—
561C22×C4—98no—
562C22×C4—91no—
563C22×C4—91no—
564C22×C4—94no—
565C22×C4—91no—
566C22×C4—91no—
567C22×C4—184no—
568C22×C4—184no—
569C22×C4—184no—
570C22×C4—184no—
571C22×C4—184no—
572C22×C4—1832no—
573C22×C4—184no—
574C22×C4—182no—
575C22×C4—184no—
576C22×C4C2×D3211yescharacteristic
577C4⋊C4—182no—
578C4⋊C4—184no—
579C22⋊C4—34no—
580C22⋊C4—38no—
581C22⋊C4—64no—
582C22⋊C4—62no—
583C22⋊C4—184no—
584C22⋊C4—184no—
585C22⋊C4—182no—
586C22⋊C4—182no—
587C42—182no—
588C42—184no—
589C22×C3—22no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—22no—
593C22×C3—24no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—22no—
599C22×C3—24no—
600C22×C3—22no—
601C22×C3—24no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—24no—
608C22×C3—38no—
609C22×C3—42no—
610C22×C3—44no—
611C22×C3—44no—
612C22×C3—42no—
613C22×C3—44no—
614C22×C3—42no—
615C22×C3—44no—
616C22×C3—42no—
617C22×C3—41no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—42no—
623C22×C3—632no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—64no—
627C22×C3—64no—
628C22×C3—64no—
629C22×C3—64no—
630C22×C3#67⋊C414yescomplemented
631C22×C3D4×Dic314yescomplemented
632C22×C3C22×C4×D311yescharacteristic
633C22×C3C2×D3×D412yes—
634C22×C3C2×D3×D412yes—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C2×#23712yes—
638C22×C3C2×#23711yescharacteristic
639C22×C3C2×#23711yescharacteristic
640C22×C3D3×#4112yes—
641C22×C3C23×Dic311yescharacteristic
642C2×D3—232no—
643C2×D3—24no—
644C2×D3—24no—
645C2×D3—24no—
646C2×D3—24no—
647C2×D3—24no—
648C2×D3—24no—
649C2×D3D4×Dic318yescomplemented
650C3×C4—24no—
651C3×C4—22no—
652C3×C4—22no—
653C3×C4—64no—
654C3×C4—64no—
655C3×C4—122no—
656Dic3—24no—
657Dic3—24no—
658Dic3—34no—
659Dic3—34no—
660Dic3—42no—
661Dic3—64no—
662Dic3—62no—
663Dic3—62no—
664Dic3—122no—
665Dic3—122no—
666Dic3—122no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671C32C4×#12011yescharacteristic, complemented, Sylow
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—34no—
679C23—34no—
680C23—34no—
681C23—616no—
682C23—68no—
683C23—616no—
684C23—68no—
685C23—62no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—68no—
690C23C2×D3×Dic312yes—
691C23C2×D3×Dic312yescomplemented
692C23#380512yes—
693C23#381112yes—
694C23C22×D3211yescharacteristic
695D4—28no—
696D4—616no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—34no—
700C2×C4—34no—
701C2×C4—68no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—94no—
710C2×C4—92no—
711C2×C4—92no—
712C2×C4—1816no—
713C2×C4—1816no—
714C2×C4—188no—
715C2×C4—182no—
716C2×C4—182no—
717C2×C4—182no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—364no—
721C2×C4C2×D3×Dic312yescomplemented
722C2×C3—24no—
723C2×C3—24no—
724C2×C3—22no—
725C2×C3—22no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—44no—
730C2×C3—44no—
731C2×C3—42no—
732C2×C3—42no—
733C2×C3—68no—
734C2×C3C2×#67⋊C411yescharacteristic
735C2×C3C4×D3×D412yes—
736C2×C3#558612yes—
737C2×C3#558611yescharacteristic
738C2×C3D3×#12011yescharacteristic
739C2×C3D3×#12011yescharacteristic
740C2×C3#560612yes—
741C2×C3#565611yescharacteristic
742C2×C3C2×D4×Dic312yes—
743C2×C3C2×D4×Dic311yescharacteristic
744D3—28no—
745C22—24no—
746C22—24no—
747C22—22no—
748C22—22no—
749C22—24no—
750C22—22no—
751C22—38no—
752C22—42no—
753C22—41no—
754C22—41no—
755C22—632no—
756C22—64no—
757C22—64no—
758C22—64no—
759C22—64no—
760C22—64no—
761C22—64no—
762C22#67⋊Dic314yescomplemented
763C22D32×D412yes—
764C22D3×#23712yes—
765C22C22×D3×Dic311yescharacteristic
766C22C2×#380511yescharacteristic
767C22C2×#381111yescharacteristic
768C4—22no—
769C4—64no—
770C4—64no—
771C4—94no—
772C4—122no—
773C4—182no—
774C4—361no—
775C4—361no—
776C3—21no—
777C3#7465911yescharacteristic, complemented
778C3Dic3×#12011yescharacteristic, complemented
779C2—24no—
780C2—42no—
781C2—68no—
782C2D3×D4×Dic312yes—
783C2#1059513012yes—
784C2#1059516011yescharacteristic
785C2#1059527811yescharacteristic
786C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC22×D4D32
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×D3×Dic3C2semidirect
2. C2×D4×C3⋊Dic3C2semidirect
4. C2×#67⋊Dic3C2semidirect
5. C3×#5220C2semidirect
6. #10591721C2semidirect
7. #10591718C2semidirect
8. #10591706C2semidirect
9. #10591705C2semidirect
10. #10591379C2semidirect
11. #10591368C2semidirect
17. C23×C3⋊Dic3C22semidirect
25. C2×#3757C22semidirect
27. C2×C4⋊(C3⋊Dic3)C22semidirect
28. C2×C4×C3⋊Dic3C22semidirect
31. C2×C3×#217C22semidirect
32. C3×#937C4semidirect
35. C2×Dic3⋊Dic3C22semidirect
38. C2×Dic32C22semidirect
39. C3×C3⋊#95C22semidirect
40. #63579C22semidirect
41. #63579C22semidirect
54. #5220D3semidirect
71. C23×C3×D3C2×C4semidirect
75. C2×C32×D4C2×C4semidirect
80. C22×C3⋊Dic3D4semidirect
87. C2×C3×#67C2×C4semidirect
99. C2×D3×Dic3D4semidirect
106. C3×#217C2×C4semidirect
107. C3×(C2×D3)⋊C4C2×C4semidirect
151. C2×#217C2×D3semidirect
152. #937Dic3semidirect
176. C3⋊#95C2×D3semidirect
184. C23×C32C22×C4semidirect
203. C2×C32×C4C22×C4semidirect
223. C2×C3×Dic3C22×C4semidirect
254. C23×D3C2×Dic3semidirect
266. C2×C3×D4C4×D3semidirect
267. C2×C3×D4C2×Dic3semidirect
278. C2×#67C2×Dic3semidirect
336. #217C2×Dic3semidirect
339. (C2×D3)⋊C4C2×Dic3semidirect
359. C22×C32C4×D4semidirect
372. C2×C3×D3C4×D4semidirect
377. C3⋊Dic3#120semidirect
445. C23×C3C2×C4×D3semidirect
451. C23×C3C22×Dic3semidirect
487. C2×C3×C4C2×C4×D3semidirect
488. C2×C3×C4C22×Dic3semidirect
531. C2×Dic3C22×Dic3semidirect
555. C2×D4D3×Dic3semidirect
630. C22×C3#67⋊C4semidirect
631. C22×C3D4×Dic3semidirect
649. C2×D3D4×Dic3semidirect
671. C32C4×#120semidirect
691. C23C2×D3×Dic3semidirect
721. C2×C4C2×D3×Dic3semidirect
762. C22#67⋊Dic3semidirect
777. C3#74659semidirect
778. C3Dic3×#120semidirect

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C2×D4×C3⋊Dic32
C2×C3×#9372
C2×#67⋊Dic32
C3×#52202
#105917212
#105917182
#105917062
#105917052
#105913792
#105913682
Dic3×#1203
#746593