Finite Group Databasebeta

← C2×#10595159 #11900436

Subgroups — C2×#10595159 #11900436

Order 1152.

4091 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C23×#624C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic, complemented
4C2×C3×#935C211yesmaximal, characteristic, complemented
5C2×#63981C211yesmaximal, characteristic, complemented
6C2×#63961C211yesmaximal, characteristic, complemented
7C2×#63958C212yesmaximal, complemented
8C2×#63955C211yesmaximal, characteristic, complemented
9C2×#63952C212yesmaximal, complemented
10#10595159C2116yesmaximal, direct product factor
11C2×#63904C212yesmaximal, complemented
12C2×#63888C212yesmaximal, complemented
13C2×#5828—31nomaximal
14C2×#5656—31nomaximal
15C24×C3⋊D3C2211yescharacteristic
16C22×C32×D4C2211yescharacteristic
17C22×#638C2212yes—
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic, complemented
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic, complemented
23C2×C3×#237—28no—
24C2×C3×#237C2218yescomplemented
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×C3×Dic6C2211yescharacteristic, complemented
27C22×#626C2212yes—
28C22×#624—28no—
29C22×#624C2212yes—
30C22×#624C2212yes—
31C22×#624C2218yescomplemented
32C2×#3757C2211yescharacteristic
33#64146C2218yescomplemented
34C2×#3752C2212yes—
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2212yescomplemented
37C3×#935C2218yescomplemented
38C2×C3×Dic3⋊C4C2212yescomplemented
39#63981C2218yescomplemented
40C2×#3724C2212yescomplemented
41C2×Dic3⋊Dic3C2212yescomplemented
42C2×#3722C2212yes—
43#63961C2218yescomplemented
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45#63958C22116yescomplemented
46#63955C2218yescomplemented
47C2×Dic32C2212yescomplemented
48#63952C22116yescomplemented
49#63904C22116yescomplemented
50#63888C22116yescomplemented
51C22×C3×#41—31no—
52C22×#237D311yescharacteristic, complemented
53C23×C4×D3—31no—
54C23×C4×D3—31no—
55C2×C3×#123—31no—
56#5828—316no—
57C2×#946—32no—
58C2×#938—32no—
59C2×#937—31no—
60C2×#937—31no—
61C2×#937—31no—
62C2×#937—61no—
63C2×#935—31no—
64C2×#935D311yescharacteristic, complemented
65C2×#929—31no—
66C2×C4×#67—32no—
67C2×C4×#67—32no—
68C2×#926—31no—
69#5656—316no—
70C2×#896—32no—
71C2×#893—32no—
72C2×#884—32no—
73C2×#882—31no—
74C2×#67⋊C4—32no—
75C2×#877—31no—
76C24×C32C2311yescharacteristic
77C24×C32C2311yescharacteristic
78C23×C3⋊D3—24no—
79C23×C3⋊D3—28no—
80C23×C3⋊D3C2314yes—
81C23×C3⋊D3C2312yes—
82C23×C3×D3C2311yescharacteristic
83C2×C32×D4—24no—
84C2×C32×D4C2314yes—
85C22×C32×C4C2311yescharacteristic
86C2×#638—28no—
87C2×#638C2318yes—
88C22×C3⋊Dic3C2312yes—
89C2×C3×#67—24no—
90C2×C3×#67—24no—
91C2×C3×#67C2314yes—
92C2×C3×#67C2314yescomplemented
93C22×C3×Dic3—24no—
94C22×C3×Dic3—24no—
95C22×C3×Dic3D418yescomplemented
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2312yes—
98C22×C3×Dic3C2314yes—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2314yes—
103C22×C3×Dic3C2314yescomplemented
104C3×#237—232no—
105C2×C3×C4×D3—24no—
106C2×C3×C4×D3C2314yescomplemented
107C2×C3×Dic6—24no—
108C2×C3×Dic6C2314yescomplemented
109C2×#626—28no—
110C2×#626C2318yes—
111C2×#624—28no—
112C2×#624—28no—
113C2×#624—232no—
114C2×#624C2318yes—
115C2×#624C2318yes—
116#3757C2314yes—
117#3752C2318yes—
118C3×#217C2314yes—
119C3×#217C2318yescomplemented
120C3×Dic3⋊C4C2318yescomplemented
121#3724C2318yescomplemented
122Dic3⋊Dic3C2318yescomplemented
123#3722C2318yes—
124(C2×D3)⋊Dic3C2318yescomplemented
125Dic32C2318yescomplemented
126C2×#525—91noSylow
127C24×D3—31no—
128C24×D3—31no—
129C24×D3—61no—
130C2×C3×#41—38no—
131C2×C3×#41—68no—
132C22×C3×Q8—31no—
133C22×C3×D4—21no—
134C22×C3×D4—31no—
135C22×C3×D4—31no—
136C22×C3×D4C2×D311yescharacteristic
137C22×C3×D4C2×D311yescharacteristic
138C23×C3×C4—31no—
139C23×C3×C4—31no—
140C23×C3×C4—31no—
141C23×C3×C4—31no—
142C22×#67—32no—
143C22×#67—32no—
144C22×#67—32no—
145C22×#67—62no—
146C22×#67C2×D311yescharacteristic
147C22×#67C2×D311yescharacteristic, complemented
148C23×Dic3C2×D311yescharacteristic
149C23×Dic3C2×D311yescharacteristic
150C23×Dic3C2×D311yescharacteristic, complemented
151C2×#237—28no—
152C2×#237C2×D318yescomplemented
153C22×D12—32no—
154C22×C4×D3—38no—
155C22×C4×D3—32no—
156C22×C4×D3—32no—
157C22×C4×D3—32no—
158C22×C4×D3—32no—
159C22×C4×D3—38no—
160C22×C4×D3—68no—
161C22×C4×D3—68no—
162C22×C4×D3C2×D311yescharacteristic, complemented
163C22×Dic6C2×D311yescharacteristic, complemented
164C3×#123—38no—
165C2×C3×C4⋊C4—32no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—32no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—32no—
171C2×#217—61no—
172C2×#217C2×D311yescharacteristic
173C2×#217C2×D312yescomplemented
174#946—316no—
175#938—316no—
176#937—38no—
177#937—38no—
178#937—38no—
179#937—68no—
180#935—38no—
181#935C2×D318yescomplemented
182#929—38no—
183C4×#67—316no—
184C4×#67—316no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—32no—
190C2×(C2×D3)⋊C4—62no—
191#926—38no—
192C2×C4⋊Dic3—32no—
193C2×Dic3⋊C4—32no—
194C2×Dic3⋊C4—32no—
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4C2×D312yescomplemented
197C2×C4×Dic3—32no—
198C2×C4×Dic3—32no—
199#896—316no—
200#893—316no—
201#884—316no—
202#882—38no—
203#67⋊C4—316no—
204#877—38no—
205C23×C32—24no—
206C23×C32—22no—
207C23×C32—24no—
208C23×C32C2×D414yes—
209C23×C32C2412yes—
210C23×C32C2412yes—
211C23×C32C2411yescharacteristic
212C22×C3⋊D3—232no—
213C22×C3⋊D3—28no—
214C22×C3⋊D3—24no—
215C22×C3⋊D3—24no—
216C22×C3⋊D3—216no—
217C22×C3⋊D3#4118yescomplemented
218C22×C3⋊D3C2414yes—
219C22×C3×D3—22no—
220C22×C3×D3—24no—
221C22×C3×D3C2412yes—
222C32×D4—28no—
223C2×C32×C4—22no—
224C2×C32×C4C2412yes—
225#638—216no—
226C2×C3⋊Dic3—24no—
227C2×C3⋊Dic3C2414yes—
228C3×#67—28no—
229C3×#67—28no—
230C2×C3×Dic3—28no—
231C2×C3×Dic3—24no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—28no—
235C2×C3×Dic3C2×D414yes—
236C2×C3×Dic3C2×D414yes—
237C2×C3×Dic3C2×D4116yescomplemented
238C2×C3×Dic3C2414yes—
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2412yes—
241C2×C3×Dic3C2412yes—
242C2×C3×Dic3C2412yes—
243C3×C4×D3—28no—
244C3×Dic6—28no—
245#626—216no—
246#624—216no—
247#624—216no—
248C22×#41—31no—
249C24×C4—91no—
250#525—916no—
251C2×#123—31no—
252C2×#123—91no—
253C2×C22⋊Q8—92no—
254C2×#121—92no—
255C2×#120—91no—
256C2×#120—91no—
257C2×C4×D4—92no—
258C2×C4×D4—92no—
259C2×#117—91no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—31no—
263C24×C3C22×D311yescharacteristic
264C24×C3C22×D311yescharacteristic
265C24×C3C22×D311yescharacteristic
266C24×C3C22×D311yescharacteristic
267C23×D3—32no—
268C23×D3—32no—
269C23×D3—34no—
270C23×D3—34no—
271C23×D3—62no—
272C23×D3—64no—
273C23×D3—68no—
274C23×D3—68no—
275C23×D3—64no—
276C23×D3—64no—
277C23×D3—128no—
278C23×D3—124no—
279C23×D3C22×D311yescharacteristic
280C3×#41—632no—
281C2×C3×Q8—34no—
282C2×C3×Q8—64no—
283C2×C3×D4—24no—
284C2×C3×D4—24no—
285C2×C3×D4—24no—
286C2×C3×D4—34no—
287C2×C3×D4—34no—
288C2×C3×D4—44no—
289C2×C3×D4—64no—
290C2×C3×D4—64no—
291C2×C3×D4C22×D314yes—
292C2×C3×D4C22×D314yes—
293C22×C3×C4—21no—
294C22×C3×C4—38no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—34no—
298C22×C3×C4—32no—
299C22×C3×C4—31no—
300C22×C3×C4—32no—
301C22×C3×C4—34no—
302C22×C3×C4—34no—
303C22×C3×C4—34no—
304C22×C3×C4—64no—
305C22×C3×C4—64no—
306C22×C3×C4—64no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—24no—
310C2×#67—24no—
311C2×#67—38no—
312C2×#67—38no—
313C2×#67—38no—
314C2×#67—68no—
315C2×#67—68no—
316C2×#67—68no—
317C2×#67—68no—
318C2×#67—128no—
319C2×#67C22×D314yes—
320C2×#67C22×D314yescomplemented
321C22×Dic3—24no—
322C22×Dic3—24no—
323C22×Dic3—32no—
324C22×Dic3—32no—
325C22×Dic3—62no—
326C22×Dic3#6718yescomplemented
327C22×Dic3C22×D312yes—
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D312yes—
330C22×Dic3C22×D314yes—
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D314yes—
334C22×Dic3C22×D314yescomplemented
335#237—232no—
336C2×D12—38no—
337C2×D12—68no—
338C2×C4×D3—24no—
339C2×C4×D3—38no—
340C2×C4×D3—38no—
341C2×C4×D3—38no—
342C2×C4×D3—38no—
343C2×C4×D3—68no—
344C2×C4×D3—68no—
345C2×C4×D3—632no—
346C2×C4×D3—68no—
347C2×C4×D3—68no—
348C2×C4×D3—632no—
349C2×C4×D3C22×D314yescomplemented
350C2×Dic6—24no—
351C2×Dic6C22×D314yescomplemented
352C3×C4⋊C4—38no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4—38no—
355#217—34no—
356#217—34no—
357#217—38no—
358#217—64no—
359#217C22×D314yes—
360#217C22×D318yescomplemented
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4—68no—
367C4⋊Dic3—38no—
368Dic3⋊C4—38no—
369Dic3⋊C4—38no—
370Dic3⋊C4—38no—
371Dic3⋊C4C22×D318yescomplemented
372C4×Dic3—38no—
373C4×Dic3—38no—
374C22×C32—28no—
375C22×C32—24no—
376C22×C32—22no—
377C22×C32—24no—
378C22×C32—44no—
379C22×C32C22×D414yes—
380C22×C32C22×D412yes—
381C22×C32C2×#4114yes—
382C22×C32C2511yescharacteristic
383C2×C3⋊D3—232no—
384C2×C3⋊D3—216no—
385C2×C3⋊D3—24no—
386C2×C3⋊D3—24no—
387C2×C3⋊D3C2×#4118yescomplemented
388C2×C3×D3—22no—
389C2×C3×D3—24no—
390C2×C3×D3—44no—
391C32×C4—22no—
392C3⋊Dic3—24no—
393C3×Dic3—24no—
394C3×Dic3—22no—
395C3×Dic3—24no—
396C3×Dic3C22×D414yes—
397C3×Dic3C22×D414yes—
398C25—91no—
399C2×#41—38no—
400C2×#41—68no—
401C22×Q8—31no—
402C22×D4—31no—
403C22×D4—31no—
404C22×D4—92no—
405C22×D4—92no—
406C22×D4D3211yescharacteristic
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—92no—
412C23×C4—92no—
413C23×C4—98no—
414C23×C4—188no—
415#123—38no—
416#123—98no—
417C22⋊Q8—916no—
418#121—916no—
419#120—98no—
420#120—98no—
421C4×D4—916no—
422C4×D4—916no—
423#117—98no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—92no—
426C2×C4⋊C4—92no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—32no—
429C2×C22⋊C4—92no—
430C2×C22⋊C4—92no—
431C2×C22⋊C4—91no—
432C2×C22⋊C4—92no—
433C2×C42—92no—
434C23×C3—24no—
435C23×C3—24no—
436C23×C3—22no—
437C23×C3—24no—
438C23×C3—24no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—21no—
443C23×C3—24no—
444C23×C3—32no—
445C23×C3—44no—
446C23×C3—44no—
447C23×C3—42no—
448C23×C3—62no—
449C23×C3—64no—
450C23×C3D3×D414yes—
451C23×C3C2×#6714yes—
452C23×C3C23×D312yes—
453C23×C3C23×D312yes—
454C23×C3C23×D312yes—
455C23×C3C23×D312yes—
456C23×C3C23×D311yescharacteristic
457C23×C3C23×D311yescharacteristic
458C22×D3—24no—
459C22×D3—22no—
460C22×D3—38no—
461C22×D3—38no—
462C22×D3—34no—
463C22×D3—34no—
464C22×D3—68no—
465C22×D3—64no—
466C22×D3—616no—
467C22×D3—616no—
468C22×D3—632no—
469C22×D3—632no—
470C22×D3—68no—
471C22×D3—64no—
472C22×D3—64no—
473C22×D3—64no—
474C22×D3—68no—
475C22×D3—64no—
476C22×D3—1216no—
477C22×D3—124no—
478C22×D3—124no—
479C22×D3—128no—
480C22×D3—1232no—
481C22×D3C23×D312yes—
482C3×Q8—68no—
483C3×D4—28no—
484C3×D4—28no—
485C3×D4—48no—
486C3×D4—68no—
487C3×D4—68no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—34no—
492C2×C3×C4—34no—
493C2×C3×C4—316no—
494C2×C3×C4—32no—
495C2×C3×C4—32no—
496C2×C3×C4—34no—
497C2×C3×C4—32no—
498C2×C3×C4—34no—
499C2×C3×C4—42no—
500C2×C3×C4—68no—
501C2×C3×C4—68no—
502C2×C3×C4—62no—
503C2×C3×C4—64no—
504C2×C3×C4—68no—
505C2×C3×C4—64no—
506C2×C3×C4C23×D312yes—
507C2×C3×C4C23×D312yes—
508#67—28no—
509#67—28no—
510#67—616no—
511#67—616no—
512#67—616no—
513#67—1216no—
514C2×Dic3—28no—
515C2×Dic3—24no—
516C2×Dic3—24no—
517C2×Dic3—22no—
518C2×Dic3—28no—
519C2×Dic3—34no—
520C2×Dic3—34no—
521C2×Dic3—64no—
522C2×Dic3—64no—
523C2×Dic3—64no—
524C2×Dic3—124no—
525C2×Dic3C2×#6714yes—
526C2×Dic3C2×#6714yes—
527C2×Dic3C2×#67116yescomplemented
528C2×Dic3C23×D314yes—
529C2×Dic3C23×D312yes—
530C2×Dic3C23×D314yes—
531C2×Dic3C23×D312yes—
532C2×Dic3C23×D312yes—
533D12—616no—
534C4×D3—28no—
535C4×D3—616no—
536C4×D3—616no—
537C4×D3—616no—
538C4×D3—616no—
539Dic6—28no—
540C2×C32—24no—
541C2×C32—42no—
542C2×C32#52514yescomplemented
543C2×C32C23×D411yescharacteristic
544C2×C32C22×#4112yes—
545C3⋊D3—28no—
546C3×D3—42no—
547C24—31no—
548C24—92no—
549C24—94no—
550C24—188no—
551C24—184no—
552C24C2×D3211yescharacteristic
553C24C2×D3211yescharacteristic
554#41—632no—
555C2×Q8—34no—
556C2×Q8—64no—
557C2×D4—24no—
558C2×D4—34no—
559C2×D4—34no—
560C2×D4—64no—
561C2×D4—64no—
562C2×D4—98no—
563C2×D4—98no—
564C2×D4—188no—
565C2×D4—188no—
566C2×D4C2×D3214yes—
567C22×C4—34no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—38no—
571C22×C4—34no—
572C22×C4—34no—
573C22×C4—32no—
574C22×C4—32no—
575C22×C4—31no—
576C22×C4—34no—
577C22×C4—64no—
578C22×C4—64no—
579C22×C4—64no—
580C22×C4—98no—
581C22×C4—98no—
582C22×C4—92no—
583C22×C4—188no—
584C22×C4—188no—
585C22×C4—1832no—
586C22×C4C2×D3211yescharacteristic
587C4⋊C4—38no—
588C4⋊C4—98no—
589C4⋊C4—98no—
590C22⋊C4—34no—
591C22⋊C4—38no—
592C22⋊C4—98no—
593C22⋊C4—98no—
594C22⋊C4—94no—
595C22⋊C4—98no—
596C42—98no—
597C22×C3—28no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—28no—
601C22×C3—22no—
602C22×C3—24no—
603C22×C3—24no—
604C22×C3—22no—
605C22×C3—24no—
606C22×C3—22no—
607C22×C3—24no—
608C22×C3—21no—
609C22×C3—44no—
610C22×C3—48no—
611C22×C3—44no—
612C22×C3—42no—
613C22×C3—44no—
614C22×C3—44no—
615C22×C3—62no—
616C22×C3—64no—
617C22×C3—84no—
618C22×C3—124no—
619C22×C3C2×D3×D414yes—
620C22×C3C2×D3×D412yes—
621C22×C3D3×#4114yes—
622C22×C3D3×#4114yes—
623C22×C3C22×#6714yes—
624C22×C3C22×#6712yes—
625C22×C3C24×D311yescharacteristic
626C22×C3C24×D311yescharacteristic
627C2×D3—24no—
628C2×D3—22no—
629C2×D3—38no—
630C2×D3—38no—
631C2×D3—44no—
632C2×D3—68no—
633C2×D3—632no—
634C2×D3—632no—
635C2×D3—616no—
636C2×D3—64no—
637C2×D3—64no—
638C2×D3—64no—
639C2×D3—64no—
640C2×D3—616no—
641C2×D3—124no—
642C2×D3—1216no—
643C2×D3—124no—
644C2×D3—1232no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—34no—
648C3×C4—34no—
649C3×C4—42no—
650C3×C4—62no—
651C3×C4—64no—
652C3×C4—64no—
653Dic3—24no—
654Dic3—24no—
655Dic3—22no—
656Dic3—64no—
657Dic3—64no—
658Dic3—124no—
659Dic3C22×#6714yes—
660Dic3C22×#6714yes—
661C32C2×#52511yescharacteristic, complemented, Sylow
662C23—24no—
663C23—24no—
664C23—22no—
665C23—32no—
666C23—64no—
667C23—62no—
668C23—98no—
669C23—94no—
670C23—1816no—
671C23—1832no—
672C23—184no—
673C23—188no—
674C23—184no—
675C23D3×#6714yes—
676C23C22×D3212yes—
677C23C22×D3212yes—
678C23C22×D3211yescharacteristic
679Q8—68no—
680D4—28no—
681D4—68no—
682D4—68no—
683D4—1816no—
684D4—1816no—
685C2×C4—22no—
686C2×C4—34no—
687C2×C4—34no—
688C2×C4—316no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—34no—
692C2×C4—34no—
693C2×C4—32no—
694C2×C4—68no—
695C2×C4—68no—
696C2×C4—64no—
697C2×C4—68no—
698C2×C4—64no—
699C2×C4—62no—
700C2×C4—94no—
701C2×C4—1816no—
702C2×C4—1816no—
703C2×C4—184no—
704C2×C4C22×D3212yes—
705C2×C3—24no—
706C2×C3—24no—
707C2×C3—22no—
708C2×C3—24no—
709C2×C3—21no—
710C2×C3—44no—
711C2×C3—42no—
712C2×C3—42no—
713C2×C3—82no—
714C2×C3—122no—
715C2×C3#565614yescomplemented
716C2×C3#582814yescomplemented
717C2×C3C22×D3×D411yescharacteristic
718C2×C3C2×D3×#4112yes—
719C2×C3C2×D3×#4112yes—
720C2×C3C23×#6711yescharacteristic
721D3—42no—
722D3—68no—
723D3—68no—
724D3—128no—
725C22—24no—
726C22—28no—
727C22—24no—
728C22—22no—
729C22—44no—
730C22—64no—
731C22—62no—
732C22—98no—
733C22—124no—
734C22—1832no—
735C22—184no—
736C22—1816no—
737C22—184no—
738C22#6431214yes—
739C22C2×D3×#6714yes—
740C22C2×D3×#6712yes—
741C22C23×D3211yescharacteristic
742C4—22no—
743C4—34no—
744C4—34no—
745C4—64no—
746C4—64no—
747C4—62no—
748C4—184no—
749C3—21no—
750C3C2×#565611yescharacteristic, complemented
751C3C2×#582811yescharacteristic, complemented
752C2—24no—
753C2—42no—
754C2—122no—
755C2—188no—
756C2#1059515914yesdirect product factor
757C2C2×#6431212yes—
758C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C23×#624C2semidirect
3. C2×#64146C2semidirect
4. C2×C3×#935C2semidirect
5. C2×#63981C2semidirect
6. C2×#63961C2semidirect
7. C2×#63958C2semidirect
8. C2×#63955C2semidirect
9. C2×#63952C2semidirect
10. #10595159C2direct (N × H)
11. C2×#63904C2semidirect
12. C2×#63888C2semidirect
19. C22×C3×#67C22semidirect
22. C23×C3×Dic3C22semidirect
24. C2×C3×#237C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C22×C3×Dic6C22semidirect
31. C22×#624C22semidirect
33. #64146C22semidirect
36. C2×C3×#217C22semidirect
37. C3×#935C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. #63981C22semidirect
40. C2×#3724C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
43. #63961C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. #63958C22semidirect
46. #63955C22semidirect
47. C2×Dic32C22semidirect
48. #63952C22semidirect
49. #63904C22semidirect
50. #63888C22semidirect
52. C22×#237D3semidirect
64. C2×#935D3semidirect
92. C2×C3×#67C23semidirect
95. C22×C3×Dic3D4semidirect
103. C22×C3×Dic3C23semidirect
106. C2×C3×C4×D3C23semidirect
108. C2×C3×Dic6C23semidirect
119. C3×#217C23semidirect
120. C3×Dic3⋊C4C23semidirect
121. #3724C23semidirect
122. Dic3⋊Dic3C23semidirect
124. (C2×D3)⋊Dic3C23semidirect
125. Dic32C23semidirect
147. C22×#67C2×D3semidirect
150. C23×Dic3C2×D3semidirect
152. C2×#237C2×D3semidirect
162. C22×C4×D3C2×D3semidirect
163. C22×Dic6C2×D3semidirect
173. C2×#217C2×D3semidirect
181. #935C2×D3semidirect
196. C2×Dic3⋊C4C2×D3semidirect
217. C22×C3⋊D3#41semidirect
237. C2×C3×Dic3C2×D4semidirect
320. C2×#67C22×D3semidirect
326. C22×Dic3#67semidirect
334. C22×Dic3C22×D3semidirect
349. C2×C4×D3C22×D3semidirect
351. C2×Dic6C22×D3semidirect
360. #217C22×D3semidirect
371. Dic3⋊C4C22×D3semidirect
387. C2×C3⋊D3C2×#41semidirect
527. C2×Dic3C2×#67semidirect
542. C2×C32#525semidirect
661. C32C2×#525semidirect
715. C2×C3#5656semidirect
716. C2×C3#5828semidirect
750. C3C2×#5656semidirect
751. C3C2×#5828semidirect
756. C2#10595159direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C23×#6242
C2×#641462
C2×C3×#9352
C2×#639812
C2×#639612
C2×#639582
C2×#639552
C2×#639522
#105951592
C2×#639042
C2×#638882
C2×#58283
C2×#56563