Finite Group Databasebeta

← C2×#10594892 #11900452

Subgroups — C2×#10594892 #11900452

Order 1152.

3921 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×C3×C4×D3C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64133C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5C2×#63976C212yesmaximal, complemented
6C2×Dic3×#67C212yesmaximal, complemented
7C2×#63908C211yesmaximal, characteristic, complemented
8C2×#63905C212yesmaximal, complemented
9#10594892C2116yesmaximal, direct product factor
10C2×#63879C212yesmaximal, complemented
11C2×#63857C211yesmaximal, characteristic, complemented
12C2×#63841C211yesmaximal, characteristic, complemented
13C2×#5791—31nomaximal
14C2×#5606—31nomaximal
15C24×C3×D3C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×#634C2211yescharacteristic, complemented
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic, complemented
21C22×C3×C4×D3—28no—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2218yescomplemented
27C22×#625C2212yes—
28C22×#625C2212yes—
29C22×D3×Dic3C2212yescomplemented
30C2×#3795—28no—
31C2×#3795C2218yescomplemented
32C2×#3757C2212yes—
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34#64133C2218yescomplemented
35C2×#3750C2212yescomplemented
36C3×#930C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yescomplemented
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39#63976C22116yescomplemented
40Dic3×#67C22116yescomplemented
41C2×Dic3⋊Dic3C2212yescomplemented
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45C2×Dic32C2212yescomplemented
46#63908C2218yescomplemented
47#63905C22116yescomplemented
48#63879C22116yescomplemented
49#63857C2218yescomplemented
50#63841C2218yescomplemented
51C24×C3×C4—31no—
52C22×#237—31no—
53C22×#235—31no—
54C23×C4×D3D311yescharacteristic, complemented
55C2×C3×#121—31no—
56C2×#953—32no—
57C2×#938—31no—
58C2×#937—32no—
59C2×D4×Dic3—32no—
60#5791—316no—
61C2×#930—31no—
62C2×#930D311yescharacteristic, complemented
63C2×#929—32no—
64C2×C4×#67—32no—
65C2×C4×#67—32no—
66C2×#926—31no—
67C2×#924—31no—
68C2×#924—31no—
69C2×#924—31no—
70C2×#924—61no—
71#5606—316no—
72C2×#897—31no—
73C2×#892—31no—
74C2×#883—32no—
75C2×#67⋊C4—32no—
76C24×C32C2311yescharacteristic
77C23×C3×D3—24no—
78C23×C3×D3—24no—
79C23×C3×D3—24no—
80C23×C3×D3C2312yes—
81C23×C3×D3C2314yes—
82C23×C3×D3C2311yescharacteristic
83C23×C3×D3C2311yescharacteristic
84C22×C32×C4—24no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2314yes—
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2312yes—
89C22×C3⋊Dic3C2312yes—
90C2×#634—24no—
91C2×#634C2314yescomplemented
92C2×C3×#67—28no—
93C2×C3×#67C2318yes—
94C22×C3×Dic3—24no—
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2314yes—
98C22×C3×Dic3C2311yescharacteristic
99C2×C3×D12—24no—
100C2×C3×D12C2314yescomplemented
101C2×C3×C4×D3—24no—
102C2×C3×C4×D3—24no—
103C2×C3×C4×D3—24no—
104C2×C3×C4×D3—232no—
105C2×C3×C4×D3D418yescomplemented
106C2×C3×C4×D3C2314yes—
107C2×C3×C4×D3C2314yes—
108C2×C3×C4×D3C2314yes—
109C2×C3×C4×D3C2314yes—
110C2×#625—28no—
111C2×#625—28no—
112C2×#625C2318yes—
113C2×#625C2318yes—
114C2×D3×Dic3—28no—
115C2×D3×Dic3C2318yescomplemented
116#3795—232no—
117#3757C2318yes—
118C4⋊(C3⋊Dic3)C2314yescomplemented
119#3750C2318yescomplemented
120C3×(C2×D3)⋊C4C2318yescomplemented
121C3×C4⋊Dic3C2314yescomplemented
122Dic3⋊Dic3C2318yescomplemented
123(C2×D3)⋊Dic3C2318yes—
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yescomplemented
126Dic32C2318yescomplemented
127C2×#525—91noSylow
128C25×C3—31no—
129C24×D3C2×D311yescharacteristic
130C22×C3×D4—32no—
131C22×C3×D4—31no—
132C23×C3×C4—21no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C23×C3×C4—31no—
136C23×C3×C4—31no—
137C23×C3×C4—31no—
138C23×C3×C4—38no—
139C23×C3×C4—68no—
140C23×C3×C4C2×D311yescharacteristic
141C23×C3×C4C2×D311yescharacteristic
142C22×#67—32no—
143C22×#67—32no—
144C22×#67—32no—
145C22×#67—32no—
146C22×#67C2×D312yes—
147C23×Dic3—32no—
148C23×Dic3C2×D311yescharacteristic
149C2×#237—38no—
150C2×#237—68no—
151C2×#235—38no—
152C2×#235—68no—
153C22×D12C2×D311yescharacteristic, complemented
154C22×C4×D3—28no—
155C22×C4×D3—32no—
156C22×C4×D3C2×D311yescharacteristic
157C22×C4×D3C2×D311yescharacteristic
158C22×C4×D3C2×D311yescharacteristic
159C22×C4×D3C2×D311yescharacteristic
160C22×C4×D3C2×D318yescomplemented
161C22×Dic6—31no—
162C22×Dic6—31no—
163C22×Dic6—61no—
164C3×#121—38no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C22⋊C4—32no—
167#953—316no—
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—32no—
171C2×#217—32no—
172C2×#217—32no—
173C2×#217—62no—
174#938—38no—
175#937—316no—
176D4×Dic3—316no—
177#930—38no—
178#930C2×D318yescomplemented
179#929—316no—
180C4×#67—316no—
181C4×#67—316no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4C2×D312yescomplemented
186#926—38no—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3—31no—
189C2×C4⋊Dic3—32no—
190C2×C4⋊Dic3—61no—
191C2×C4⋊Dic3C2×D311yescharacteristic, complemented
192#924—38no—
193#924—38no—
194#924—38no—
195#924—68no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4—32no—
198C2×Dic3⋊C4—32no—
199C2×Dic3⋊C4—62no—
200C2×C4×Dic3—32no—
201C2×C4×Dic3—32no—
202#897—38no—
203#892—38no—
204#883—316no—
205#67⋊C4—316no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32#4114yescomplemented
209C23×C32C2412yes—
210C23×C32C2411yescharacteristic
211C22×C3×D3—232no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—22no—
216C22×C3×D3—28no—
217C22×C3×D3—28no—
218C22×C3×D3—28no—
219C22×C3×D3—24no—
220C22×C3×D3—24no—
221C22×C3×D3—24no—
222C22×C3×D3C2×D414yes—
223C22×C3×D3#4114yescomplemented
224C22×C3×D3C2414yes—
225C22×C3×D3C2412yes—
226C22×C3×D3C2412yes—
227C2×C32×C4—22no—
228C2×C32×C4—28no—
229C2×C32×C4C2×D414yes—
230C2×C32×C4C2412yes—
231C2×C32×C4C2412yes—
232C2×C3⋊Dic3—24no—
233C2×C3⋊Dic3—24no—
234C2×C3⋊Dic3C2414yes—
235C2×C3⋊Dic3C2414yes—
236#634—28no—
237C3×#67—216no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—24no—
240C2×C3×Dic3—28no—
241C2×C3×Dic3C2×D414yes—
242C2×C3×Dic3C2414yes—
243C2×C3×Dic3C2412yes—
244C2×C3×Dic3C2412yes—
245C3×D12—28no—
246C3×C4×D3—28no—
247C3×C4×D3—28no—
248C3×C4×D3—28no—
249C3×C4×D3C2×D4116yescomplemented
250#625—216no—
251#625—216no—
252D3×Dic3—216no—
253C22×#41—91no—
254C24×C4—31no—
255#525—916no—
256C2×#123—92no—
257C2×C22⋊Q8—91no—
258C2×C22⋊Q8—91no—
259C2×#121—31no—
260C2×#121—91no—
261C2×#120—92no—
262C2×C4×D4—92no—
263C2×C4×D4—92no—
264C2×#117—91no—
265C24×C3—21no—
266C24×C3—31no—
267C24×C3—31no—
268C24×C3—34no—
269C24×C3—32no—
270C24×C3—64no—
271C24×C3—64no—
272C24×C3—64no—
273C24×C3C22×D311yescharacteristic
274C24×C3C22×D311yescharacteristic
275C23×D3—24no—
276C23×D3—24no—
277C23×D3—24no—
278C23×D3C22×D312yes—
279C23×D3C22×D314yes—
280C23×D3C22×D311yescharacteristic
281C23×D3C22×D311yescharacteristic
282C2×C3×D4—38no—
283C2×C3×D4—34no—
284C2×C3×D4—68no—
285C2×C3×D4—64no—
286C22×C3×C4—24no—
287C22×C3×C4—24no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—24no—
291C22×C3×C4—31no—
292C22×C3×C4—38no—
293C22×C3×C4—34no—
294C22×C3×C4—32no—
295C22×C3×C4—31no—
296C22×C3×C4—34no—
297C22×C3×C4—34no—
298C22×C3×C4—34no—
299C22×C3×C4—34no—
300C22×C3×C4—44no—
301C22×C3×C4—64no—
302C22×C3×C4—632no—
303C22×C3×C4—64no—
304C22×C3×C4—64no—
305C22×C3×C4—64no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D314yes—
309C22×C3×C4C22×D314yes—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—28no—
313C2×#67—38no—
314C2×#67—38no—
315C2×#67—38no—
316C2×#67—38no—
317C2×#67—68no—
318C2×#67—68no—
319C2×#67—68no—
320C2×#67—68no—
321C2×#67C22×D318yes—
322C22×Dic3—24no—
323C22×Dic3—32no—
324C22×Dic3—32no—
325C22×Dic3—32no—
326C22×Dic3—32no—
327C22×Dic3—38no—
328C22×Dic3—62no—
329C22×Dic3—62no—
330C22×Dic3—68no—
331C22×Dic3C22×D312yes—
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D314yes—
334C22×Dic3C22×D311yescharacteristic
335#237—632no—
336#235—632no—
337C2×D12—24no—
338C2×D12C22×D314yescomplemented
339C2×C4×D3—24no—
340C2×C4×D3—24no—
341C2×C4×D3—24no—
342C2×C4×D3—232no—
343C2×C4×D3—38no—
344C2×C4×D3—68no—
345C2×C4×D3#6718yescomplemented
346C2×C4×D3C22×D314yes—
347C2×C4×D3C22×D314yes—
348C2×C4×D3C22×D314yes—
349C2×C4×D3C22×D314yes—
350C2×Dic6—34no—
351C2×Dic6—34no—
352C2×Dic6—64no—
353C2×Dic6—64no—
354C2×Dic6—64no—
355C2×Dic6—124no—
356C3×C4⋊C4—34no—
357C3×C22⋊C4—38no—
358#217—38no—
359#217—38no—
360#217—38no—
361#217—38no—
362#217—38no—
363#217—68no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4—38no—
367(C2×D3)⋊C4C22×D318yescomplemented
368C4⋊Dic3—34no—
369C4⋊Dic3—34no—
370C4⋊Dic3—38no—
371C4⋊Dic3—64no—
372C4⋊Dic3C22×D314yescomplemented
373Dic3⋊C4—38no—
374Dic3⋊C4—38no—
375Dic3⋊C4—38no—
376Dic3⋊C4—68no—
377C4×Dic3—38no—
378C4×Dic3—38no—
379C22×C32—28no—
380C22×C32—22no—
381C22×C32—22no—
382C22×C32C22×D412yes—
383C22×C32C2×#4112yes—
384C22×C32C2×#4112yes—
385C22×C32C2×#4114yescomplemented
386C22×C32C2511yescharacteristic
387C2×C3×D3—232no—
388C2×C3×D3—28no—
389C2×C3×D3—28no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—22no—
393C2×C3×D3—22no—
394C2×C3×D3—24no—
395C2×C3×D3—24no—
396C2×C3×D3—24no—
397C2×C3×D3—48no—
398C2×C3×D3C22×D414yes—
399C2×C3×D3C2×#4114yescomplemented
400C32×C4—22no—
401C32×C4C22×D414yes—
402C3⋊Dic3—24no—
403C3⋊Dic3—24no—
404C3×Dic3—22no—
405C3×Dic3—24no—
406C3×Dic3C22×D414yes—
407C25—31no—
408C2×#41—98no—
409C2×#41—188no—
410C22×Q8—91no—
411C22×D4—32no—
412C22×D4—31no—
413C22×D4—92no—
414C22×D4—92no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—31no—
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—38no—
421C23×C4—68no—
422C23×C4—92no—
423C23×C4D3211yescharacteristic
424#123—916no—
425C22⋊Q8—98no—
426C22⋊Q8—98no—
427#121—38no—
428#121—98no—
429#120—916no—
430C4×D4—916no—
431C4×D4—916no—
432#117—98no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—92no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—92no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—92no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—92no—
441C2×C22⋊C4—92no—
442C2×C42—92no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—21no—
449C23×C3—24no—
450C23×C3—34no—
451C23×C3—34no—
452C23×C3—32no—
453C23×C3—32no—
454C23×C3—34no—
455C23×C3—42no—
456C23×C3—42no—
457C23×C3—68no—
458C23×C3—68no—
459C23×C3—632no—
460C23×C3—62no—
461C23×C3—62no—
462C23×C3—62no—
463C23×C3—68no—
464C23×C3—62no—
465C23×C3—64no—
466C23×C3—64no—
467C23×C3—64no—
468C23×C3#23514yescomplemented
469C23×C3#23714yescomplemented
470C23×C3C23×D312yes—
471C23×C3C23×D312yes—
472C23×C3C23×D311yescharacteristic
473C23×C3C23×D311yescharacteristic
474C22×D3—232no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—28no—
479C22×D3—22no—
480C22×D3—28no—
481C22×D3—28no—
482C22×D3—24no—
483C22×D3—24no—
484C22×D3—24no—
485C22×D3#23514yescomplemented
486C22×D3C2×#6714yes—
487C22×D3C23×D314yes—
488C22×D3C23×D312yes—
489C22×D3C23×D312yes—
490C3×D4—616no—
491C3×D4—68no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—28no—
495C2×C3×C4—28no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—24no—
499C2×C3×C4—34no—
500C2×C3×C4—32no—
501C2×C3×C4—316no—
502C2×C3×C4—34no—
503C2×C3×C4—32no—
504C2×C3×C4—48no—
505C2×C3×C4—42no—
506C2×C3×C4—68no—
507C2×C3×C4—68no—
508C2×C3×C4—68no—
509C2×C3×C4—64no—
510C2×C3×C4—62no—
511C2×C3×C4—68no—
512C2×C3×C4D3×D414yes—
513C2×C3×C4C2×#6714yes—
514C2×C3×C4C23×D312yes—
515C2×C3×C4C23×D312yes—
516C2×C3×C4C23×D312yes—
517C2×C3×C4C23×D312yes—
518#67—216no—
519#67—616no—
520#67—616no—
521#67—616no—
522#67—616no—
523C2×Dic3—24no—
524C2×Dic3—22no—
525C2×Dic3—28no—
526C2×Dic3—34no—
527C2×Dic3—34no—
528C2×Dic3—34no—
529C2×Dic3—34no—
530C2×Dic3—64no—
531C2×Dic3—64no—
532C2×Dic3—64no—
533C2×Dic3—64no—
534C2×Dic3—64no—
535C2×Dic3—64no—
536C2×Dic3—616no—
537C2×Dic3—124no—
538C2×Dic3—124no—
539C2×Dic3C2×#6714yes—
540C2×Dic3C23×D314yes—
541C2×Dic3C23×D312yes—
542C2×Dic3C23×D312yes—
543D12—28no—
544C4×D3—28no—
545C4×D3—28no—
546C4×D3—28no—
547C4×D3—616no—
548C4×D3C2×#67116yescomplemented
549Dic6—68no—
550Dic6—68no—
551Dic6—128no—
552C2×C32—24no—
553C2×C32#52514yescomplemented
554C2×C32C23×D411yescharacteristic
555C2×C32C22×#4111yescharacteristic
556C2×C32C22×#4111yescharacteristic
557C3×D3—24no—
558C3×D3—24no—
559C3×D3—44no—
560C24—31no—
561C24—31no—
562C24—34no—
563C24—32no—
564C24—64no—
565C24—64no—
566C24—64no—
567C24C2×D3211yescharacteristic
568#41—1832no—
569C2×Q8—94no—
570C2×Q8—184no—
571C2×D4—38no—
572C2×D4—34no—
573C2×D4—68no—
574C2×D4—64no—
575C2×D4—98no—
576C2×D4—98no—
577C2×D4—188no—
578C2×D4—188no—
579C22×C4—24no—
580C22×C4—31no—
581C22×C4—34no—
582C22×C4—38no—
583C22×C4—34no—
584C22×C4—32no—
585C22×C4—31no—
586C22×C4—34no—
587C22×C4—34no—
588C22×C4—34no—
589C22×C4—64no—
590C22×C4—632no—
591C22×C4—64no—
592C22×C4—64no—
593C22×C4—64no—
594C22×C4—98no—
595C22×C4—92no—
596C22×C4—92no—
597C22×C4—188no—
598C22×C4C2×D3214yes—
599C22×C4C2×D3211yescharacteristic
600C22×C4C2×D3211yescharacteristic
601C4⋊C4—34no—
602C4⋊C4—98no—
603C4⋊C4—94no—
604C4⋊C4—98no—
605C22⋊C4—38no—
606C22⋊C4—98no—
607C22⋊C4—98no—
608C22⋊C4—98no—
609C22⋊C4—98no—
610C42—98no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—28no—
616C22×C3—28no—
617C22×C3—22no—
618C22×C3—24no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—34no—
623C22×C3—34no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—48no—
627C22×C3—632no—
628C22×C3—62no—
629C22×C3—62no—
630C22×C3—62no—
631C22×C3—62no—
632C22×C3—68no—
633C22×C3—68no—
634C22×C3—64no—
635C22×C3—64no—
636C22×C3—64no—
637C22×C3—128no—
638C22×C3C2×#23512yes—
639C22×C3C2×#23512yes—
640C22×C3C2×#23514yescomplemented
641C22×C3C2×D3×D412yes—
642C22×C3C2×#23712yes—
643C22×C3C2×#23714yescomplemented
644C22×C3D3×#4112yes—
645C22×C3C22×#6712yes—
646C22×C3C24×D311yescharacteristic
647C22×C3C24×D311yescharacteristic
648C2×D3—232no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—28no—
654C2×D3—28no—
655C2×D3—24no—
656C2×D3—24no—
657C2×D3—24no—
658C2×D3—48no—
659C2×D3C2×#23514yescomplemented
660C2×D3C22×#6714yes—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—24no—
664C3×C4—34no—
665C3×C4—42no—
666C3×C4—64no—
667C3×C4—62no—
668C3×C4C2×D3×D414yes—
669C3×C4C22×#6714yes—
670Dic3—24no—
671Dic3—22no—
672Dic3—64no—
673Dic3—64no—
674Dic3—64no—
675Dic3—64no—
676Dic3—124no—
677Dic3—124no—
678Dic3C22×#6714yes—
679C32C2×#52511yescharacteristic, complemented, Sylow
680C23—22no—
681C23—22no—
682C23—34no—
683C23—34no—
684C23—32no—
685C23—32no—
686C23—34no—
687C23—68no—
688C23—68no—
689C23—632no—
690C23—62no—
691C23—62no—
692C23—68no—
693C23—62no—
694C23—62no—
695C23—64no—
696C23—64no—
697C23—64no—
698C23#379514yescomplemented
699C23C22×D3212yes—
700C23C22×D3211yescharacteristic
701Q8—188no—
702D4—616no—
703D4—68no—
704D4—1816no—
705D4—1816no—
706C2×C4—22no—
707C2×C4—28no—
708C2×C4—34no—
709C2×C4—32no—
710C2×C4—316no—
711C2×C4—34no—
712C2×C4—32no—
713C2×C4—68no—
714C2×C4—68no—
715C2×C4—68no—
716C2×C4—64no—
717C2×C4—62no—
718C2×C4—68no—
719C2×C4—94no—
720C2×C4—94no—
721C2×C4—1816no—
722C2×C4—184no—
723C2×C4—184no—
724C2×C4D3×#6714yes—
725C2×C4C22×D3212yes—
726C2×C4C22×D3212yes—
727C2×C3—24no—
728C2×C3—24no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—24no—
732C2×C3—21no—
733C2×C3—44no—
734C2×C3—64no—
735C2×C3—64no—
736C2×C3—124no—
737C2×C3#560614yescomplemented
738C2×C3#579114yescomplemented
739C2×C3C22×#23511yescharacteristic
740C2×C3C22×#23511yescharacteristic
741C2×C3C22×D3×D411yescharacteristic
742C2×C3C22×#23711yescharacteristic
743C2×C3C2×D3×#4111yescharacteristic
744C2×C3C23×#6711yescharacteristic
745D3—24no—
746D3—24no—
747D3—44no—
748C22—22no—
749C22—28no—
750C22—22no—
751C22—34no—
752C22—34no—
753C22—632no—
754C22—62no—
755C22—62no—
756C22—62no—
757C22—68no—
758C22—68no—
759C22—62no—
760C22—64no—
761C22—64no—
762C22—64no—
763C22—128no—
764C22C2×#379512yes—
765C22C2×#379514yescomplemented
766C22D3×#23512yes—
767C22C2×D3×#6712yes—
768C22C23×D3211yescharacteristic
769C4—22no—
770C4—34no—
771C4—64no—
772C4—62no—
773C4—184no—
774C4—184no—
775C4C2×D3×#6714yes—
776C3—21no—
777C3C2×#560611yescharacteristic, complemented
778C3C2×#579111yescharacteristic, complemented
779C2—24no—
780C2—64no—
781C2—64no—
782C2—124no—
783C2#1059489214yesdirect product factor
784C2C22×#379511yescharacteristic
785C2C2×D3×#23511yescharacteristic
786C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
2. C22×#3795C2semidirect
3. C2×#64133C2semidirect
4. C2×C3×#930C2semidirect
5. C2×#63976C2semidirect
6. C2×Dic3×#67C2semidirect
7. C2×#63908C2semidirect
8. C2×#63905C2semidirect
9. #10594892C2direct (N × H)
10. C2×#63879C2semidirect
11. C2×#63857C2semidirect
12. C2×#63841C2semidirect
17. C22×#634C22semidirect
20. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
29. C22×D3×Dic3C22semidirect
31. C2×#3795C22semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. #64133C22semidirect
35. C2×#3750C22semidirect
36. C3×#930C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. #63976C22semidirect
40. Dic3×#67C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×Dic32C22semidirect
46. #63908C22semidirect
47. #63905C22semidirect
48. #63879C22semidirect
49. #63857C22semidirect
50. #63841C22semidirect
54. C23×C4×D3D3semidirect
62. C2×#930D3semidirect
91. C2×#634C23semidirect
100. C2×C3×D12C23semidirect
105. C2×C3×C4×D3D4semidirect
115. C2×D3×Dic3C23semidirect
118. C4⋊(C3⋊Dic3)C23semidirect
119. #3750C23semidirect
120. C3×(C2×D3)⋊C4C23semidirect
121. C3×C4⋊Dic3C23semidirect
122. Dic3⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
126. Dic32C23semidirect
153. C22×D12C2×D3semidirect
160. C22×C4×D3C2×D3semidirect
178. #930C2×D3semidirect
185. C2×(C2×D3)⋊C4C2×D3semidirect
191. C2×C4⋊Dic3C2×D3semidirect
208. C23×C32#41semidirect
223. C22×C3×D3#41semidirect
249. C3×C4×D3C2×D4semidirect
338. C2×D12C22×D3semidirect
345. C2×C4×D3#67semidirect
367. (C2×D3)⋊C4C22×D3semidirect
372. C4⋊Dic3C22×D3semidirect
385. C22×C32C2×#41semidirect
399. C2×C3×D3C2×#41semidirect
468. C23×C3#235semidirect
469. C23×C3#237semidirect
485. C22×D3#235semidirect
548. C4×D3C2×#67semidirect
553. C2×C32#525semidirect
640. C22×C3C2×#235semidirect
643. C22×C3C2×#237semidirect
659. C2×D3C2×#235semidirect
679. C32C2×#525semidirect
698. C23#3795semidirect
737. C2×C3#5606semidirect
738. C2×C3#5791semidirect
765. C22C2×#3795semidirect
777. C3C2×#5606semidirect
778. C3C2×#5791semidirect
783. C2#10594892direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C22×#37952
C2×#641332
C2×C3×#9302
C2×#639762
C2×Dic3×#672
C2×#639082
C2×#639052
#105948922
C2×#638792
C2×#638572
C2×#638412
C2×#57913
C2×#56063