Finite Group Databasebeta

← C2×#10595524 #11900968

Subgroups — C2×#10595524 #11900968

Order 1152.

4299 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic, complemented
2C22×D3×#67C211yesmaximal, characteristic, complemented
3C2×#64162C211yesmaximal, characteristic, complemented
4C2×C3×#953C211yesmaximal, characteristic, complemented
5#10595524C2116yesmaximal, direct product factor
6C2×#63983C212yesmaximal, complemented
7C2×#63971C212yesmaximal, complemented
8C2×#63970C212yesmaximal, complemented
9C2×#63969C212yesmaximal, complemented
10C2×D3×#217C211yesmaximal, characteristic, complemented
11C2×#63966C211yesmaximal, characteristic, complemented
12C2×#63961C211yesmaximal, characteristic, complemented
13C2×#5804—31nomaximal
14C2×#5589—31nomaximal
15C25×C32C2211yescharacteristic, complemented
16C24×C3×D3C2211yescharacteristic
17C23×D32C2211yescharacteristic, complemented
18C22×#638C2211yescharacteristic
19C22×#638C2212yescomplemented
20C22×C3×#67—28no—
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2212yes—
23C22×C3×#67C2212yescomplemented
24C22×C3×#67C2212yescomplemented
25C22×C3×#67C2218yescomplemented
26C23×C3×Dic3C2211yescharacteristic, complemented
27C2×D3×#67—28no—
28C2×D3×#67C2218yescomplemented
29C22×#626C2211yescharacteristic, complemented
30C22×#625C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32C22×D3×Dic3C2212yescomplemented
33#64162C2218yescomplemented
34C2×#3757C2211yescharacteristic, complemented
35C2×#3757C2212yescomplemented
36C3×#953C2218yescomplemented
37C2×C3×#217C2211yescharacteristic, complemented
38C2×C3×#217C2212yescomplemented
39#63983C22116yescomplemented
40#63971C22116yescomplemented
41#63970C22116yescomplemented
42#63969C22116yescomplemented
43D3×#217C2218yescomplemented
44C2×#3724C2212yescomplemented
45#63966C2218yescomplemented
46C2×Dic3⋊Dic3C2212yescomplemented
47C2×#3722C2212yescomplemented
48#63961C2218yescomplemented
49C2×(C2×D3)⋊Dic3C2212yescomplemented
50C2×(C2×D3)⋊Dic3C2212yescomplemented
51C23×C3×D4—31no—
52C23×#67—31no—
53C23×#67D311yescharacteristic, complemented
54C22×D3×D4—31no—
55C2×C3×#120—31no—
56C2×#953—31no—
57C2×#953—31no—
58C2×#953—61no—
59C2×#953D311yescharacteristic, complemented
60C22×#217—31no—
61#5804—316no—
62C2×#939—32no—
63C2×#939—32no—
64C2×#938—32no—
65C2×#937—32no—
66C2×#937—32no—
67C2×#935—31no—
68C2×#935—32no—
69C2×#929—31no—
70C2×#929—31no—
71#5589—316no—
72C2×#886—31no—
73C2×#884—32no—
74C2×#883—32no—
75C2×D3×C22⋊C4—31no—
76C24×C32—24no—
77C24×C32—44no—
78C24×C32C2312yes—
79C24×C32C2311yescharacteristic
80C24×C32C2314yescomplemented
81C23×C3⋊D3C2311yescharacteristic
82C23×C3×D3—44no—
83C23×C3×D3D418yescomplemented
84C23×C3×D3C2311yescharacteristic
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2314yes—
88C22×D32—24no—
89C22×D32—44no—
90C22×D32C2314yescomplemented
91C2×#638—24no—
92C2×#638—44no—
93C2×#638C2314yes—
94C2×#638C2318yescomplemented
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2312yes—
97C2×C3×#67—24no—
98C2×C3×#67—28no—
99C2×C3×#67—28no—
100C2×C3×#67—232no—
101C2×C3×#67—44no—
102C2×C3×#67C2314yes—
103C2×C3×#67C2318yes—
104C2×C3×#67C2318yescomplemented
105C2×C3×#67C2318yescomplemented
106C22×C3×Dic3—24no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2312yes—
109C22×C3×Dic3C2312yes—
110C22×C3×Dic3C2314yescomplemented
111D3×#67—232no—
112C2×#626—24no—
113C2×#626C2314yescomplemented
114C2×#625—24no—
115C2×#625C2314yescomplemented
116C2×D3×Dic3—24no—
117C2×D3×Dic3—44no—
118C2×D3×Dic3C2314yescomplemented
119C2×D3×Dic3C2318yescomplemented
120#3757C2314yescomplemented
121#3757C2318yescomplemented
122C3×#217C2314yescomplemented
123C3×#217C2318yescomplemented
124#3724C2318yescomplemented
125Dic3⋊Dic3C2318yescomplemented
126#3722C2318yescomplemented
127(C2×D3)⋊Dic3C2318yescomplemented
128(C2×D3)⋊Dic3C2318yescomplemented
129C2×#534—91noSylow
130C25×C3—21no—
131C25×C3—31no—
132C25×C3C2×D311yescharacteristic, complemented
133C25×C3C2×D311yescharacteristic, complemented
134C24×D3—31no—
135C24×D3—31no—
136C24×D3C2×D311yescharacteristic
137C22×C3×D4—31no—
138C22×C3×D4—32no—
139C22×C3×D4—32no—
140C22×C3×D4—38no—
141C22×C3×D4—32no—
142C22×C3×D4—68no—
143C23×C3×C4—31no—
144C22×#67—28no—
145C22×#67—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—32no—
150C22×#67—32no—
151C22×#67—38no—
152C22×#67—31no—
153C22×#67—61no—
154C22×#67—62no—
155C22×#67—68no—
156C22×#67C2×D311yescharacteristic
157C22×#67C2×D312yes—
158C22×#67C2×D312yescomplemented
159C22×#67C2×D312yescomplemented
160C22×#67C2×D318yescomplemented
161C23×Dic3—31no—
162C23×Dic3—32no—
163C23×Dic3C2×D311yescharacteristic, complemented
164C2×D3×D4—38no—
165C2×D3×D4—68no—
166C22×D12—31no—
167C22×C4×D3—31no—
168C22×C4×D3—32no—
169C3×#120—38no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—32no—
172#953—38no—
173#953—38no—
174#953—68no—
175#953C2×D318yescomplemented
176C2×#217—31no—
177C2×#217—32no—
178C2×#217—31no—
179C2×#217—32no—
180C2×#217—32no—
181C2×#217—32no—
182C2×#217—38no—
183C2×#217—61no—
184C2×#217—62no—
185C2×#217C2×D311yescharacteristic, complemented
186C2×#217C2×D312yescomplemented
187#939—316no—
188#939—316no—
189#938—316no—
190#937—316no—
191#937—316no—
192#935—38no—
193#935—316no—
194#929—38no—
195#929—38no—
196C2×(C2×D3)⋊C4—32no—
197C2×(C2×D3)⋊C4—32no—
198C2×(C2×D3)⋊C4—32no—
199C2×(C2×D3)⋊C4—32no—
200C2×C4⋊Dic3—32no—
201C2×Dic3⋊C4—32no—
202C2×Dic3⋊C4—32no—
203C2×Dic3⋊C4—32no—
204#886—38no—
205#884—316no—
206#883—316no—
207D3×C22⋊C4—38no—
208C23×C32—24no—
209C23×C32—24no—
210C23×C32—24no—
211C23×C32—28no—
212C23×C32—24no—
213C23×C32—48no—
214C23×C32—416no—
215C23×C32C2×D414yes—
216C23×C32C2414yes—
217C23×C32C2412yes—
218C23×C32C2411yescharacteristic
219C22×C3⋊D3—22no—
220C22×C3⋊D3—24no—
221C22×C3⋊D3C2412yes—
222C22×C3×D3—24no—
223C22×C3×D3—24no—
224C22×C3×D3—22no—
225C22×C3×D3—24no—
226C22×C3×D3—416no—
227C22×C3×D3—48no—
228C22×C3×D3C2×D414yes—
229C22×C3×D3C2×D414yes—
230C22×C3×D3C2×D4116yescomplemented
231C22×C3×D3C2412yes—
232C22×C3×D3C2412yes—
233C22×C3×D3C2412yes—
234C2×D32—28no—
235C2×D32—48no—
236C2×D32—416no—
237#638—28no—
238#638—48no—
239C2×C3⋊Dic3—22no—
240C2×C3⋊Dic3—24no—
241C2×C3⋊Dic3C2414yes—
242C2×C3⋊Dic3C2412yes—
243C3×#67—28no—
244C3×#67—216no—
245C3×#67—216no—
246C3×#67—48no—
247C2×C3×Dic3—22no—
248C2×C3×Dic3—24no—
249C2×C3×Dic3—28no—
250C2×C3×Dic3—24no—
251C2×C3×Dic3C2414yes—
252C2×C3×Dic3C2414yes—
253C2×C3×Dic3C2412yes—
254#626—28no—
255#625—28no—
256D3×Dic3—28no—
257D3×Dic3—48no—
258C23×D4—31no—
259C23×D4—91no—
260#534—916no—
261C2×#123—91no—
262C2×#123—92no—
263C2×#123—91no—
264C2×#121—92no—
265C2×#121—92no—
266C2×#120—31no—
267C2×#120—92no—
268C2×#120—91no—
269C22×C22⋊C4—91no—
270C24×C3—24no—
271C24×C3—24no—
272C24×C3—22no—
273C24×C3—21no—
274C24×C3—24no—
275C24×C3—31no—
276C24×C3—31no—
277C24×C3—38no—
278C24×C3—34no—
279C24×C3—31no—
280C24×C3—44no—
281C24×C3—44no—
282C24×C3—44no—
283C24×C3—48no—
284C24×C3—124no—
285C24×C3C22×D312yes—
286C24×C3C22×D312yes—
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C24×C3C22×D314yescomplemented
290C24×C3C22×D314yescomplemented
291C23×D3—31no—
292C23×D3—31no—
293C23×D3—34no—
294C23×D3—34no—
295C23×D3—44no—
296C23×D3—61no—
297C23×D3—64no—
298C23×D3—64no—
299C23×D3—124no—
300C23×D3—124no—
301C23×D3#6718yescomplemented
302C23×D3C22×D311yescharacteristic
303C23×D3C22×D311yescharacteristic
304C23×D3C22×D311yescharacteristic
305C23×D3C22×D314yes—
306C2×C3×D4—38no—
307C2×C3×D4—34no—
308C2×C3×D4—38no—
309C2×C3×D4—38no—
310C2×C3×D4—68no—
311C2×C3×D4—68no—
312C2×C3×D4—632no—
313C2×C3×D4—64no—
314C2×C3×D4—124no—
315C22×C3×C4—32no—
316C22×C3×C4—31no—
317C22×C3×C4—32no—
318C22×C3×C4—34no—
319C22×C3×C4—64no—
320C2×#67—24no—
321C2×#67—28no—
322C2×#67—28no—
323C2×#67—232no—
324C2×#67—34no—
325C2×#67—34no—
326C2×#67—34no—
327C2×#67—34no—
328C2×#67—38no—
329C2×#67—38no—
330C2×#67—34no—
331C2×#67—44no—
332C2×#67—64no—
333C2×#67—68no—
334C2×#67—64no—
335C2×#67—632no—
336C2×#67—64no—
337C2×#67—64no—
338C2×#67—64no—
339C2×#67—64no—
340C2×#67—124no—
341C2×#67—124no—
342C2×#67—124no—
343C2×#67—128no—
344C2×#67C22×D318yes—
345C2×#67C22×D314yes—
346C2×#67C22×D318yescomplemented
347C2×#67C22×D318yescomplemented
348C22×Dic3—24no—
349C22×Dic3—31no—
350C22×Dic3—32no—
351C22×Dic3—32no—
352C22×Dic3—31no—
353C22×Dic3—34no—
354C22×Dic3—38no—
355C22×Dic3—62no—
356C22×Dic3—61no—
357C22×Dic3—64no—
358C22×Dic3—124no—
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D312yes—
361C22×Dic3C22×D312yes—
362C22×Dic3C22×D314yescomplemented
363D3×D4—632no—
364C2×D12—34no—
365C2×D12—64no—
366C2×C4×D3—34no—
367C2×C4×D3—38no—
368C2×C4×D3—64no—
369C2×C4×D3—124no—
370C3×C22⋊C4—34no—
371C3×C22⋊C4—38no—
372#217—34no—
373#217—38no—
374#217—34no—
375#217—38no—
376#217—38no—
377#217—38no—
378#217—64no—
379#217—68no—
380#217C22×D314yescomplemented
381#217C22×D318yescomplemented
382(C2×D3)⋊C4—38no—
383(C2×D3)⋊C4—38no—
384(C2×D3)⋊C4—38no—
385(C2×D3)⋊C4—38no—
386C4⋊Dic3—38no—
387Dic3⋊C4—38no—
388Dic3⋊C4—38no—
389Dic3⋊C4—38no—
390C22×C32—24no—
391C22×C32—28no—
392C22×C32—24no—
393C22×C32—24no—
394C22×C32—24no—
395C22×C32—416no—
396C22×C32—48no—
397C22×C32C22×D414yes—
398C22×C32C22×D412yes—
399C22×C32H(5,𝔽2)14yes—
400C22×C32C2511yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—24no—
403C2×C3⋊D3—44no—
404C2×C3×D3—28no—
405C2×C3×D3—28no—
406C2×C3×D3—24no—
407C2×C3×D3—24no—
408C2×C3×D3—22no—
409C2×C3×D3—24no—
410C2×C3×D3—416no—
411C2×C3×D3—44no—
412C2×C3×D3C22×D414yes—
413C2×C3×D3C22×D414yes—
414D32—416no—
415C3⋊Dic3—22no—
416C3⋊Dic3—24no—
417C3×Dic3—22no—
418C3×Dic3—24no—
419C3×Dic3—24no—
420C25—31no—
421C25—91no—
422C25D3211yescharacteristic, complemented
423C22×D4—31no—
424C22×D4—32no—
425C22×D4—32no—
426C22×D4—38no—
427C22×D4—32no—
428C22×D4—68no—
429C22×D4—91no—
430C22×D4—98no—
431C22×D4—91no—
432C22×D4—91no—
433C22×D4—92no—
434C22×D4—188no—
435C23×C4—31no—
436C23×C4—91no—
437C23×C4—92no—
438#123—98no—
439#123—916no—
440#123—98no—
441#121—916no—
442#121—916no—
443#120—38no—
444#120—916no—
445#120—98no—
446C2×C4⋊C4—92no—
447C2×C4⋊C4—92no—
448C2×C22⋊C4—31no—
449C2×C22⋊C4—32no—
450C2×C22⋊C4—98no—
451C2×C22⋊C4—92no—
452C2×C22⋊C4—92no—
453C2×C22⋊C4—92no—
454C2×C22⋊C4—91no—
455C2×C22⋊C4—92no—
456C23×C3—24no—
457C23×C3—24no—
458C23×C3—28no—
459C23×C3—24no—
460C23×C3—28no—
461C23×C3—24no—
462C23×C3—24no—
463C23×C3—24no—
464C23×C3—24no—
465C23×C3—24no—
466C23×C3—28no—
467C23×C3—24no—
468C23×C3—22no—
469C23×C3—21no—
470C23×C3—24no—
471C23×C3—34no—
472C23×C3—34no—
473C23×C3—32no—
474C23×C3—32no—
475C23×C3—316no—
476C23×C3—32no—
477C23×C3—44no—
478C23×C3—44no—
479C23×C3—48no—
480C23×C3—44no—
481C23×C3—48no—
482C23×C3—48no—
483C23×C3—416no—
484C23×C3—416no—
485C23×C3—416no—
486C23×C3—432no—
487C23×C3—64no—
488C23×C3—64no—
489C23×C3—64no—
490C23×C3—62no—
491C23×C3—128no—
492C23×C3—1216no—
493C23×C3D3×D414yes—
494C23×C3C2×#6714yes—
495C23×C3C23×D314yes—
496C23×C3C23×D314yes—
497C23×C3C23×D312yes—
498C23×C3C23×D312yes—
499C23×C3C23×D311yescharacteristic
500C23×C3C23×D311yescharacteristic
501C22×D3—24no—
502C22×D3—24no—
503C22×D3—22no—
504C22×D3—24no—
505C22×D3—32no—
506C22×D3—32no—
507C22×D3—416no—
508C22×D3—48no—
509C22×D3—62no—
510C22×D3—68no—
511C22×D3—62no—
512C22×D3—64no—
513C22×D3—64no—
514C22×D3—62no—
515C22×D3—68no—
516C22×D3—122no—
517C22×D3—124no—
518C22×D3—128no—
519C22×D3—128no—
520C22×D3—1216no—
521C22×D3—1216no—
522C22×D3C2×#6714yes—
523C22×D3C2×#6714yes—
524C22×D3C2×#67116yescomplemented
525C22×D3C23×D312yes—
526C22×D3C23×D312yes—
527C22×D3C23×D312yes—
528C3×D4—616no—
529C3×D4—616no—
530C3×D4—68no—
531C3×D4—128no—
532C2×C3×C4—34no—
533C2×C3×C4—32no—
534C2×C3×C4—34no—
535C2×C3×C4—68no—
536C2×C3×C4—64no—
537C2×C3×C4—64no—
538C2×C3×C4—62no—
539#67—28no—
540#67—216no—
541#67—216no—
542#67—48no—
543#67—68no—
544#67—68no—
545#67—68no—
546#67—68no—
547#67—68no—
548#67—128no—
549#67—128no—
550#67—128no—
551#67—1216no—
552C2×Dic3—22no—
553C2×Dic3—24no—
554C2×Dic3—24no—
555C2×Dic3—28no—
556C2×Dic3—32no—
557C2×Dic3—34no—
558C2×Dic3—34no—
559C2×Dic3—32no—
560C2×Dic3—64no—
561C2×Dic3—62no—
562C2×Dic3—68no—
563C2×Dic3—62no—
564C2×Dic3—64no—
565C2×Dic3—64no—
566C2×Dic3—62no—
567C2×Dic3—122no—
568C2×Dic3—124no—
569C2×Dic3—128no—
570C2×Dic3C23×D312yes—
571C2×Dic3C23×D314yes—
572C2×Dic3C23×D314yes—
573D12—68no—
574C4×D3—68no—
575C4×D3—128no—
576C2×C32—24no—
577C2×C32—44no—
578C2×C32#53414yescomplemented
579C2×C32C23×D411yescharacteristic
580C2×C32C2×H(5,𝔽2)12yes—
581C3⋊D3—42no—
582C3×D3—24no—
583C3×D3—24no—
584C3×D3—42no—
585C24—24no—
586C24—31no—
587C24—31no—
588C24—34no—
589C24—38no—
590C24—31no—
591C24—44no—
592C24—94no—
593C24—91no—
594C24—124no—
595C24—184no—
596C24—364no—
597C24C2×D3212yes—
598C24C2×D3211yescharacteristic
599C24C2×D3214yescomplemented
600C2×D4—34no—
601C2×D4—38no—
602C2×D4—38no—
603C2×D4—38no—
604C2×D4—68no—
605C2×D4—68no—
606C2×D4—632no—
607C2×D4—64no—
608C2×D4—94no—
609C2×D4—94no—
610C2×D4—94no—
611C2×D4—98no—
612C2×D4—124no—
613C2×D4—184no—
614C2×D4—1832no—
615C2×D4—184no—
616C2×D4—184no—
617C2×D4—364no—
618C22×C4—34no—
619C22×C4—32no—
620C22×C4—31no—
621C22×C4—32no—
622C22×C4—64no—
623C22×C4—94no—
624C22×C4—98no—
625C22×C4—92no—
626C22×C4—91no—
627C22×C4—184no—
628C22×C4—364no—
629C4⋊C4—98no—
630C4⋊C4—98no—
631C22⋊C4—34no—
632C22⋊C4—38no—
633C22⋊C4—98no—
634C22⋊C4—98no—
635C22⋊C4—98no—
636C22⋊C4—94no—
637C22⋊C4—98no—
638C22×C3—24no—
639C22×C3—24no—
640C22×C3—28no—
641C22×C3—28no—
642C22×C3—28no—
643C22×C3—24no—
644C22×C3—24no—
645C22×C3—24no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—22no—
650C22×C3—24no—
651C22×C3—24no—
652C22×C3—21no—
653C22×C3—34no—
654C22×C3—34no—
655C22×C3—44no—
656C22×C3—48no—
657C22×C3—44no—
658C22×C3—44no—
659C22×C3—416no—
660C22×C3—416no—
661C22×C3—416no—
662C22×C3—432no—
663C22×C3—48no—
664C22×C3—48no—
665C22×C3—64no—
666C22×C3—64no—
667C22×C3—68no—
668C22×C3—68no—
669C22×C3—64no—
670C22×C3—62no—
671C22×C3—1216no—
672C22×C3—124no—
673C22×C3C2×D3×D414yes—
674C22×C3C2×D3×D412yes—
675C22×C3#100414yes—
676C22×C3#100414yes—
677C22×C3C22×#6714yes—
678C22×C3C22×#6712yes—
679C22×C3C24×D311yescharacteristic
680C22×C3C24×D311yescharacteristic
681C2×D3—24no—
682C2×D3—24no—
683C2×D3—28no—
684C2×D3—28no—
685C2×D3—22no—
686C2×D3—24no—
687C2×D3—416no—
688C2×D3—44no—
689C2×D3—62no—
690C2×D3—64no—
691C2×D3—64no—
692C2×D3—62no—
693C2×D3—122no—
694C2×D3—124no—
695C2×D3—1216no—
696C2×D3—1216no—
697C2×D3—124no—
698C2×D3—124no—
699C2×D3—244no—
700C2×D3C22×#6714yes—
701C2×D3C22×#6714yes—
702C3×C4—64no—
703C3×C4—64no—
704C3×C4—62no—
705Dic3—22no—
706Dic3—24no—
707Dic3—24no—
708Dic3—62no—
709Dic3—64no—
710Dic3—64no—
711Dic3—62no—
712Dic3—122no—
713Dic3—124no—
714C32C2×#53411yescharacteristic, complemented, Sylow
715C23—24no—
716C23—24no—
717C23—28no—
718C23—24no—
719C23—24no—
720C23—34no—
721C23—34no—
722C23—32no—
723C23—32no—
724C23—316no—
725C23—32no—
726C23—48no—
727C23—416no—
728C23—64no—
729C23—64no—
730C23—62no—
731C23—64no—
732C23—92no—
733C23—128no—
734C23—1216no—
735C23—188no—
736C23—182no—
737C23—184no—
738C23—368no—
739C23—3616no—
740C23D3×#6714yes—
741C23C22×D3214yes—
742C23C22×D3212yes—
743C23C22×D3211yescharacteristic
744D4—616no—
745D4—616no—
746D4—68no—
747D4—128no—
748D4—188no—
749D4—188no—
750D4—188no—
751D4—368no—
752C2×C4—34no—
753C2×C4—32no—
754C2×C4—34no—
755C2×C4—68no—
756C2×C4—64no—
757C2×C4—62no—
758C2×C4—64no—
759C2×C4—94no—
760C2×C4—92no—
761C2×C4—188no—
762C2×C4—182no—
763C2×C4—184no—
764C2×C4—368no—
765C2×C3—24no—
766C2×C3—24no—
767C2×C3—21no—
768C2×C3—22no—
769C2×C3—24no—
770C2×C3—44no—
771C2×C3—48no—
772C2×C3—44no—
773C2×C3—44no—
774C2×C3—64no—
775C2×C3—64no—
776C2×C3—122no—
777C2×C3#558914yescomplemented
778C2×C3#580414yescomplemented
779C2×C3C22×D3×D411yescharacteristic
780C2×C3C2×#100412yes—
781C2×C3C2×#100412yes—
782C2×C3C23×#6711yescharacteristic
783D3—24no—
784D3—24no—
785D3—42no—
786D3—122no—
787D3—122no—
788D3—242no—
789C22—24no—
790C22—28no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—34no—
795C22—34no—
796C22—416no—
797C22—48no—
798C22—64no—
799C22—64no—
800C22—68no—
801C22—68no—
802C22—62no—
803C22—64no—
804C22—1216no—
805C22—124no—
806C22—182no—
807C22—184no—
808C22—3616no—
809C22—364no—
810C22C2×D3×#6714yes—
811C22C2×D3×#6712yes—
812C22#6433014yes—
813C22C23×D3211yescharacteristic
814C4—64no—
815C4—62no—
816C4—64no—
817C4—182no—
818C4—184no—
819C3—21no—
820C3C2×#558911yescharacteristic, complemented
821C3C2×#580411yescharacteristic, complemented
822C2—24no—
823C2—44no—
824C2—64no—
825C2—64no—
826C2—122no—
827C2—362no—
828C2#1059552414yesdirect product factor
829C2C22×D3×#6711yescharacteristic
830C2C2×#6433012yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC25×C32C22
socleC23×C32C24
hypercenterC25D32
hypocenterC32C2×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C23×C3×#67C2semidirect
2. C22×D3×#67C2semidirect
3. C2×#64162C2semidirect
4. C2×C3×#953C2semidirect
5. #10595524C2direct (N × H)
6. C2×#63983C2semidirect
7. C2×#63971C2semidirect
8. C2×#63970C2semidirect
9. C2×#63969C2semidirect
10. C2×D3×#217C2semidirect
11. C2×#63966C2semidirect
12. C2×#63961C2semidirect
15. C25×C32C22semidirect
17. C23×D32C22semidirect
19. C22×#638C22semidirect
23. C22×C3×#67C22semidirect
24. C22×C3×#67C22semidirect
25. C22×C3×#67C22semidirect
26. C23×C3×Dic3C22semidirect
28. C2×D3×#67C22semidirect
29. C22×#626C22semidirect
30. C22×#625C22semidirect
31. C22×D3×Dic3C22semidirect
32. C22×D3×Dic3C22semidirect
33. #64162C22semidirect
34. C2×#3757C22semidirect
35. C2×#3757C22semidirect
36. C3×#953C22semidirect
37. C2×C3×#217C22semidirect
38. C2×C3×#217C22semidirect
39. #63983C22semidirect
40. #63971C22semidirect
41. #63970C22semidirect
42. #63969C22semidirect
43. D3×#217C22semidirect
44. C2×#3724C22semidirect
45. #63966C22semidirect
46. C2×Dic3⋊Dic3C22semidirect
47. C2×#3722C22semidirect
48. #63961C22semidirect
49. C2×(C2×D3)⋊Dic3C22semidirect
50. C2×(C2×D3)⋊Dic3C22semidirect
53. C23×#67D3semidirect
59. C2×#953D3semidirect
80. C24×C32C23semidirect
83. C23×C3×D3D4semidirect
90. C22×D32C23semidirect
94. C2×#638C23semidirect
104. C2×C3×#67C23semidirect
105. C2×C3×#67C23semidirect
110. C22×C3×Dic3C23semidirect
113. C2×#626C23semidirect
115. C2×#625C23semidirect
118. C2×D3×Dic3C23semidirect
119. C2×D3×Dic3C23semidirect
120. #3757C23semidirect
121. #3757C23semidirect
122. C3×#217C23semidirect
123. C3×#217C23semidirect
124. #3724C23semidirect
125. Dic3⋊Dic3C23semidirect
126. #3722C23semidirect
127. (C2×D3)⋊Dic3C23semidirect
128. (C2×D3)⋊Dic3C23semidirect
132. C25×C3C2×D3semidirect
133. C25×C3C2×D3semidirect
158. C22×#67C2×D3semidirect
159. C22×#67C2×D3semidirect
160. C22×#67C2×D3semidirect
163. C23×Dic3C2×D3semidirect
175. #953C2×D3semidirect
185. C2×#217C2×D3semidirect
186. C2×#217C2×D3semidirect
230. C22×C3×D3C2×D4semidirect
289. C24×C3C22×D3semidirect
290. C24×C3C22×D3semidirect
301. C23×D3#67semidirect
346. C2×#67C22×D3semidirect
347. C2×#67C22×D3semidirect
362. C22×Dic3C22×D3semidirect
380. #217C22×D3semidirect
381. #217C22×D3semidirect
422. C25D32semidirect
524. C22×D3C2×#67semidirect
578. C2×C32#534semidirect
599. C24C2×D32semidirect
714. C32C2×#534semidirect
777. C2×C3#5589semidirect
778. C2×C3#5804semidirect
820. C3C2×#5589semidirect
821. C3C2×#5804semidirect
828. C2#10595524direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×D3×#672
C2×#641622
C2×C3×#9532
#105955242
C2×#639832
C2×#639712
C2×#639702
C2×#639692
C2×D3×#2172
C2×#639662
C2×#639612
C2×#58043
C2×#55893