Finite Group Databasebeta

← #11801995

Subgroups — #11801995

Order 1152.

2591 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic3C211yesmaximal, characteristic, complemented
2C2×#63977C211yesmaximal, characteristic
3C2×#63952C211yesmaximal, characteristic, complemented
4C2×#63880C212yesmaximal, complemented
5#10592657C211yesmaximal, characteristic, complemented
6C3×#4955C211yesmaximal, characteristic, complemented
7C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
8#10591719C211yesmaximal, characteristic, complemented
9#10591373C212yesmaximal, complemented
10Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
11#10591364C212yesmaximal, complemented
12#73818—31nomaximal
13C4×#882—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×#626C2212yes—
19C22×#624C2211yescharacteristic, complemented
20C22×D3×Dic3—24no—
21C22×D3×Dic3—28no—
22C22×D3×Dic3C2212yes—
23C22×D3×Dic3C2212yes—
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3752C2212yescomplemented
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×C4×Dic3C2212yescomplemented
31#63977C418yescomplemented
32C2×#3724C2211yescharacteristic, complemented
33C2×Dic3⋊Dic3C2212yescomplemented
34C2×#3722C2211yescharacteristic, complemented
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×Dic32C2211yescharacteristic, complemented
37#63952—24no—
38#63880—28no—
39#63658C2212yescomplemented
40C3×C3⋊#95C2212yescomplemented
41#63579C2212yescomplemented
42C24×Dic3—31no—
43C23×C4×D3—31no—
44C2×#953—31no—
45C2×C4×#67—31no—
46C2×#882—31no—
47C2×#67⋊C4—31no—
48C2×#67⋊C4—32no—
49C2×C4×D12—32no—
50C3×#379—31no—
51C3×C4×C22⋊C4—31no—
52#4958—31no—
53#4958—31no—
54#4958—32no—
55#4958—61no—
56#4955D311yescharacteristic, complemented
57#4950—31no—
58#4946—31no—
59#4946—32no—
60Dic3×C22⋊C4—32no—
61Dic3×C22⋊C4D311yescharacteristic, complemented
62C4×(C2×D3)⋊C4—32no—
63#4668—32no—
64#4665—32no—
65C24×C32C2311yescharacteristic
66C23×C3⋊D3C2311yescharacteristic
67C23×C3×D3—22no—
68C23×C3×D3—22no—
69C23×C3×D3—24no—
70C23×C3×D3—24no—
71C23×C3×D3C2×C414yescomplemented
72C23×C3×D3C2312yes—
73C22×C32×C4C2312yes—
74C2×#638—22no—
75C2×#638—22no—
76C2×#638C2×C414yescomplemented
77C22×C3⋊Dic3—22no—
78C22×C3⋊Dic3—24no—
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3×Dic3—24no—
82C22×C3×Dic3D414yescomplemented
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C2×#626—24no—
89C2×#626—24no—
90C2×#626C2×C418yescomplemented
91C2×#624—24no—
92C2×#624—22no—
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
100C32×C22⋊C4—22no—
101#3752—24no—
102C3×#217—22no—
103C3×#217C2×C414yescomplemented
104C3×(C2×D3)⋊C4—24no—
105C3×(C2×D3)⋊C4—24no—
106C3×C4×Dic3—24no—
107#3724—22no—
108Dic3⋊Dic3—24no—
109#3722—22no—
110(C2×D3)⋊Dic3C2×C418yescomplemented
111Dic32—22no—
112C4×#120—91noSylow
113C25×C3—31no—
114C24×D3C2×D311yescharacteristic
115C23×C3×C4—31no—
116C22×#67—31no—
117C22×#67—31no—
118C22×#67—32no—
119C22×#67—61no—
120C23×Dic3—32no—
121C23×Dic3—31no—
122C23×Dic3—31no—
123C23×Dic3—32no—
124C23×Dic3—61no—
125C23×Dic3—68no—
126C23×Dic3—64no—
127C23×Dic3C2×D311yescharacteristic
128C22×D12—32no—
129C22×C4×D3—32no—
130C22×C4×D3—32no—
131C22×C4×D3—31no—
132C22×C4×D3—31no—
133C22×C4×D3—68no—
134C22×C4×D3—64no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—32no—
139C2×C3×C22⋊C4—32no—
140C2×C3×C22⋊C4C2×D311yescharacteristic
141C2×C3×C22⋊C4C2×D311yescharacteristic
142C2×C3×C42—32no—
143#953—38no—
144C2×#217—32no—
145C2×#217C2×D311yescharacteristic
146C2×#217C2×D311yescharacteristic
147C4×#67—64no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—62no—
154C2×(C2×D3)⋊C4C2×D312yes—
155C2×(C2×D3)⋊C4C2×D312yes—
156C2×C4⋊Dic3—32no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3C2×D312yescomplemented
163#882—38no—
164#67⋊C4—68no—
165#67⋊C4—64no—
166C4×D12—68no—
167C3×#95—32no—
168C3⋊#95—32no—
169C3⋊#95—32no—
170C3⋊#95—32no—
171C3⋊#95—32no—
172C3⋊#95—62no—
173C3⋊#95C2×D312yescomplemented
174C23×C32—22no—
175C23×C32—22no—
176C23×C32C22×C412yes—
177C23×C32C2×D412yes—
178C23×C32#4112yes—
179C23×C32C2411yescharacteristic
180C22×C3⋊D3—21no—
181C22×C3⋊D3—22no—
182C22×C3⋊D3—22no—
183C22×C3⋊D3—21no—
184C22×C3⋊D3C22×C412yescomplemented
185C22×C3×D3—216no—
186C22×C3×D3—28no—
187C22×C3×D3—28no—
188C22×C3×D3—28no—
189C22×C3×D3—22no—
190C22×C3×D3—22no—
191C22×C3×D3—22no—
192C22×C3×D3—22no—
193C22×C3×D3—216no—
194C22×C3×D3C22×C414yes—
195C22×C3×D3C2×D414yes—
196C22×C3×D3#4114yes—
197C2×C32×C4—22no—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
200#638—28no—
201C2×C3⋊Dic3—28no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3C22×C412yescomplemented
207C2×C3⋊Dic3C2×D414yes—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—28no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3C22×C414yescomplemented
217C2×C3×Dic3C2×D412yes—
218C2×C3×Dic3C2×D412yes—
219C2×C3×Dic3C2×D414yes—
220#626—216no—
221#624—44no—
222D3×Dic3—216no—
223D3×Dic3—216no—
224C24×C4—91no—
225C2×#120—91no—
226C2×C4×D4—92no—
227C2×C4×D4—91no—
228#386—92no—
229#386—91no—
230#385—92no—
231#385—91no—
232#379—31no—
233C4×C22⋊C4—31no—
234C4×C22⋊C4—92no—
235C24×C3—21no—
236C24×C3—32no—
237C24×C3—34no—
238C24×C3—64no—
239C24×C3—64no—
240C24×C3—62no—
241C24×C3—62no—
242C24×C3C22×D311yescharacteristic
243C24×C3C22×D311yescharacteristic
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—24no—
247C23×D3—24no—
248C23×D3—31no—
249C23×D3—31no—
250C23×D3—61no—
251C23×D3C4×D314yescomplemented
252C23×D3C22×D312yes—
253C22×C3×C4—22no—
254C22×C3×C4—31no—
255C22×C3×C4—34no—
256C22×C3×C4—32no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—64no—
261C22×C3×C4C22×D312yes—
262C22×C3×C4C22×D312yes—
263C2×#67—34no—
264C2×#67—34no—
265C2×#67—38no—
266C2×#67—64no—
267C2×#67—64no—
268C2×#67—64no—
269C2×#67—62no—
270C2×#67—62no—
271C2×#67—62no—
272C2×#67—62no—
273C2×#67—122no—
274C2×#67—122no—
275C22×Dic3—24no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—32no—
279C22×Dic3—32no—
280C22×Dic3—38no—
281C22×Dic3—61no—
282C22×Dic3—62no—
283C22×Dic3—64no—
284C22×Dic3—64no—
285C22×Dic3—632no—
286C22×Dic3—64no—
287C22×Dic3—64no—
288C22×Dic3—62no—
289C22×Dic3—62no—
290C22×Dic3—64no—
291C22×Dic3—64no—
292C22×Dic3—64no—
293C22×Dic3—124no—
294C22×Dic3—122no—
295C22×Dic3D1214yescomplemented
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D312yes—
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D311yescharacteristic
301C2×D12—38no—
302C2×D12—64no—
303C2×D12—64no—
304C2×C4×D3—38no—
305C2×C4×D3—64no—
306C2×C4×D3—64no—
307C2×C4×D3—64no—
308C2×C4×D3—64no—
309C2×C4×D3—632no—
310C2×C4×D3—64no—
311C2×C4×D3—64no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C2×C4×D3—64no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—22no—
317C3×C22⋊C4—34no—
318C3×C22⋊C4—42no—
319C3×C22⋊C4—64no—
320C3×C22⋊C4—64no—
321C3×C22⋊C4—62no—
322C3×C42—64no—
323#217—22no—
324#217—38no—
325#217C4×D314yescomplemented
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—38no—
329(C2×D3)⋊C4—62no—
330(C2×D3)⋊C4—64no—
331(C2×D3)⋊C4—64no—
332(C2×D3)⋊C4—62no—
333(C2×D3)⋊C4—124no—
334C4⋊Dic3—64no—
335Dic3⋊C4—64no—
336Dic3⋊C4—62no—
337Dic3⋊C4—62no—
338C4×Dic3—24no—
339C4×Dic3—62no—
340C4×Dic3—62no—
341C22×C32—24no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32—24no—
345C22×C32C4×D414yescomplemented
346C22×C32C23×C411yescharacteristic
347C22×C32C22×D411yescharacteristic
348C22×C32C22×D412yes—
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4112yes—
351C2×C3⋊D3—24no—
352C2×C3⋊D3—22no—
353C2×C3⋊D3—41no—
354C2×C3⋊D3—41no—
355C2×C3⋊D3—42no—
356C2×C3×D3—232no—
357C2×C3×D3—24no—
358C2×C3×D3—24no—
359C2×C3×D3—24no—
360C2×C3×D3—24no—
361C2×C3×D3—24no—
362C2×C3×D3—24no—
363C2×C3×D3C4×D418yescomplemented
364C32×C4—42no—
365C3⋊Dic3—22no—
366C3⋊Dic3—24no—
367C3×Dic3—24no—
368C3×Dic3—22no—
369C3×Dic3—41no—
370C3×Dic3—41no—
371C3×Dic3#12014yescomplemented
372C25—31no—
373C22×D4—92no—
374C22×D4—91no—
375C23×C4—31no—
376C23×C4—91no—
377C23×C4—92no—
378C23×C4—92no—
379C23×C4—91no—
380C23×C4—184no—
381C23×C4—188no—
382#120—98no—
383C4×D4—188no—
384C4×D4—184no—
385C2×C4⋊C4—91no—
386C2×C4⋊C4—92no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—32no—
391C2×C22⋊C4—92no—
392C2×C22⋊C4—91no—
393C2×C22⋊C4—92no—
394C2×C22⋊C4D3211yescharacteristic
395C2×C42—32no—
396C2×C42—91no—
397#95—32no—
398#95—92no—
399#95—92no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—21no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—34no—
409C23×C3—34no—
410C23×C3—34no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—616no—
414C23×C3—68no—
415C23×C3—68no—
416C23×C3—616no—
417C23×C3—68no—
418C23×C3—62no—
419C23×C3—62no—
420C23×C3—62no—
421C23×C3—62no—
422C23×C3C2×C4×D312yes—
423C23×C3C2×C4×D312yes—
424C23×C3C2×D1212yes—
425C23×C3#23512yes—
426C23×C3D3×D412yes—
427C23×C3#23712yes—
428C23×C3C23×D311yescharacteristic
429C23×C3C23×D311yescharacteristic
430C22×D3—28no—
431C22×D3—216no—
432C22×D3—28no—
433C22×D3—28no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—22no—
437C22×D3—22no—
438C22×D3—216no—
439C22×D3—32no—
440C22×D3—32no—
441C22×D3—62no—
442C22×D3—61no—
443C22×D3—61no—
444C22×D3—62no—
445C22×D3—61no—
446C22×D3—62no—
447C22×D3—62no—
448C22×D3—61no—
449C22×D3—62no—
450C22×D3—122no—
451C22×D3—121no—
452C22×D3—121no—
453C22×D3—122no—
454C22×D3C2×C4×D314yes—
455C22×D3D3×D414yes—
456C22×D3#23714yes—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—32no—
464C2×C3×C4—34no—
465C2×C3×C4—34no—
466C2×C3×C4—32no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—68no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478#67—616no—
479#67—68no—
480#67—68no—
481#67—128no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—28no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—32no—
491C2×Dic3—32no—
492C2×Dic3—34no—
493C2×Dic3—34no—
494C2×Dic3—62no—
495C2×Dic3—64no—
496C2×Dic3—616no—
497C2×Dic3—68no—
498C2×Dic3—68no—
499C2×Dic3—61no—
500C2×Dic3—62no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—62no—
504C2×Dic3—62no—
505C2×Dic3—62no—
506C2×Dic3—61no—
507C2×Dic3—616no—
508C2×Dic3—122no—
509C2×Dic3—122no—
510C2×Dic3—121no—
511C2×Dic3—121no—
512C2×Dic3—128no—
513C2×Dic3C2×C4×D314yescomplemented
514C2×Dic3C2×D1212yes—
515C2×Dic3C2×D1212yes—
516C2×Dic3D3×D414yes—
517D12—616no—
518C4×D3—616no—
519C4×D3—616no—
520C4×D3—124no—
521C4×D3—124no—
522C2×C32—24no—
523C2×C32C2×C4×D411yescharacteristic
524C2×C32C2×C4×D412yes—
525C2×C32C2×#12011yescharacteristic
526C2×C32#52511yescharacteristic
527C2×C32#52512yes—
528C3⋊D3—42no—
529C3×D3—28no—
530C24—32no—
531C24—34no—
532C24—64no—
533C24—64no—
534C24—62no—
535C24—62no—
536C24—91no—
537C24C2×D3211yescharacteristic
538C2×D4—98no—
539C2×D4—94no—
540C2×D4—184no—
541C2×D4—184no—
542C2×D4—182no—
543C2×D4—182no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—32no—
547C22×C4—34no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—64no—
551C22×C4—98no—
552C22×C4—91no—
553C22×C4—92no—
554C22×C4—182no—
555C22×C4—184no—
556C22×C4—184no—
557C22×C4—184no—
558C22×C4—184no—
559C22×C4—184no—
560C22×C4—184no—
561C22×C4—1832no—
562C22×C4—184no—
563C22×C4—182no—
564C22×C4C2×D3212yes—
565C4⋊C4—182no—
566C4⋊C4—184no—
567C22⋊C4—22no—
568C22⋊C4—34no—
569C22⋊C4—64no—
570C22⋊C4—64no—
571C22⋊C4—62no—
572C22⋊C4—98no—
573C22⋊C4—184no—
574C22⋊C4—182no—
575C42—64no—
576C42—182no—
577C22×C3—24no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—22no—
583C22×C3—24no—
584C22×C3—22no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—21no—
590C22×C3—24no—
591C22×C3—38no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—632no—
597C22×C3—64no—
598C22×C3—64no—
599C22×C3—64no—
600C22×C3—64no—
601C22×C3—64no—
602C22×C3—64no—
603C22×C3C4×D1214yescomplemented
604C22×C3#67⋊C414yescomplemented
605C22×C3C22×C4×D311yescharacteristic
606C22×C3C22×C4×D311yescharacteristic
607C22×C3C22×D1211yescharacteristic
608C22×C3C2×#23511yescharacteristic
609C22×C3C2×D3×D411yescharacteristic
610C22×C3C2×D3×D412yes—
611C22×C3C2×D3×D412yes—
612C22×C3C2×#23712yes—
613C22×C3C2×#23711yescharacteristic
614C22×C3D3×#4112yes—
615C2×D3—232no—
616C2×D3—24no—
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—24no—
621C2×D3—24no—
622C2×D3—62no—
623C2×D3—64no—
624C2×D3—62no—
625C2×D3—64no—
626C2×D3—122no—
627C2×D3—124no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—122no—
631C2×D3—121no—
632C2×D3—122no—
633C2×D3—121no—
634C2×D3—241no—
635C2×D3—242no—
636C2×D3—241no—
637C2×D3#67⋊C418yescomplemented
638C3×C4—34no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—64no—
642C3×C4—62no—
643C3×C4—82no—
644C3×C4—121no—
645C3×C4—121no—
646Dic3—22no—
647Dic3—24no—
648Dic3—41no—
649Dic3—41no—
650Dic3—62no—
651Dic3—62no—
652Dic3—64no—
653Dic3—64no—
654Dic3—124no—
655Dic3—122no—
656Dic3#88214yescomplemented
657C32C4×#12011yescharacteristic, complemented, Sylow
658C23—22no—
659C23—22no—
660C23—34no—
661C23—34no—
662C23—34no—
663C23—616no—
664C23—68no—
665C23—68no—
666C23—616no—
667C23—62no—
668C23—62no—
669C23—62no—
670C23—62no—
671C23—68no—
672C23—92no—
673C23—181no—
674C23—182no—
675C23—182no—
676C23—181no—
677C23C4×D3212yes—
678C23D3×D1212yes—
679C23#380412yes—
680C23C22×D3211yescharacteristic
681D4—1816no—
682D4—188no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—32no—
687C2×C4—34no—
688C2×C4—34no—
689C2×C4—32no—
690C2×C4—68no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—92no—
699C2×C4—94no—
700C2×C4—1816no—
701C2×C4—1816no—
702C2×C4—188no—
703C2×C4—181no—
704C2×C4—182no—
705C2×C4—182no—
706C2×C4—181no—
707C2×C4—364no—
708C2×C3—24no—
709C2×C3—24no—
710C2×C3—21no—
711C2×C3—22no—
712C2×C3—21no—
713C2×C3—22no—
714C2×C3—21no—
715C2×C3—44no—
716C2×C3—68no—
717C2×C3C2×C4×D1211yescharacteristic
718C2×C3C2×#67⋊C411yescharacteristic
719C2×C3C2×#67⋊C412yes—
720C2×C3C2×#88211yescharacteristic
721C2×C3#552411yescharacteristic
722C2×C3C4×D3×D412yes—
723C2×C3#554712yes—
724C2×C3#558611yescharacteristic
725C2×C3#558612yes—
726C2×C3D3×#12011yescharacteristic
727D3—28no—
728D3—122no—
729D3—122no—
730D3—242no—
731C22—22no—
732C22—24no—
733C22—24no—
734C22—22no—
735C22—38no—
736C22—632no—
737C22—64no—
738C22—64no—
739C22—64no—
740C22—64no—
741C22—64no—
742C22—64no—
743C22—182no—
744C22—184no—
745C22—361no—
746C22—362no—
747C22—361no—
748C22#6388014yescomplemented
749C22C2×C4×D3211yescharacteristic
750C22C2×D3×D1211yescharacteristic
751C22D32×D412yes—
752C22D3×#23712yes—
753C22C2×#380411yescharacteristic
754C4—34no—
755C4—42no—
756C4—64no—
757C4—62no—
758C4—121no—
759C4—121no—
760C4—182no—
761C4—184no—
762C3—21no—
763C3C4×#88211yescharacteristic, complemented
764C3#7381811yescharacteristic, complemented
765C2—24no—
766C2—68no—
767C2—362no—
768C2#1059407811yescharacteristic
769C2D3×#67⋊C412yes—
770C2D3×#88211yescharacteristic
771C2C2×#6388011yescharacteristic
772C2#1059512912yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63977C2
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D3×Dic3C2semidirect
3. C2×#63952C2semidirect
4. C2×#63880C2semidirect
5. #10592657C2semidirect
6. C3×#4955C2semidirect
7. C3×Dic3×C22⋊C4C2semidirect
8. #10591719C2semidirect
9. #10591373C2semidirect
10. Dic3×(C2×D3)⋊C4C2semidirect
11. #10591364C2semidirect
19. C22×#624C22semidirect
25. C2×#3752C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. #63977C4semidirect
32. C2×#3724C22semidirect
33. C2×Dic3⋊Dic3C22semidirect
34. C2×#3722C22semidirect
36. C2×Dic32C22semidirect
39. #63658C22semidirect
40. C3×C3⋊#95C22semidirect
41. #63579C22semidirect
56. #4955D3semidirect
61. Dic3×C22⋊C4D3semidirect
71. C23×C3×D3C2×C4semidirect
76. C2×#638C2×C4semidirect
82. C22×C3×Dic3D4semidirect
90. C2×#626C2×C4semidirect
99. C2×D3×Dic3D4semidirect
103. C3×#217C2×C4semidirect
110. (C2×D3)⋊Dic3C2×C4semidirect
162. C2×C4×Dic3C2×D3semidirect
173. C3⋊#95C2×D3semidirect
184. C22×C3⋊D3C22×C4semidirect
206. C2×C3⋊Dic3C22×C4semidirect
216. C2×C3×Dic3C22×C4semidirect
251. C23×D3C4×D3semidirect
295. C22×Dic3D12semidirect
325. #217C4×D3semidirect
345. C22×C32C4×D4semidirect
363. C2×C3×D3C4×D4semidirect
371. C3×Dic3#120semidirect
513. C2×Dic3C2×C4×D3semidirect
603. C22×C3C4×D12semidirect
604. C22×C3#67⋊C4semidirect
637. C2×D3#67⋊C4semidirect
656. Dic3#882semidirect
657. C32C4×#120semidirect
748. C22#63880semidirect
763. C3C4×#882semidirect
764. C3#73818semidirect

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C2×#639772
C2×#639522
C2×#638802
#105926572
C3×#49552
C3×Dic3×C22⋊C42
#105917192
#105913732
Dic3×(C2×D3)⋊C42
#105913642
#738183
C4×#8823