Finite Group Databasebeta

← C2×#10595230 #11900965

Subgroups — C2×#10595230 #11900965

Order 1152.

4139 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C23×#625C211yesmaximal, characteristic, complemented
3C2×#64144C211yesmaximal, characteristic, complemented
4C2×C3×#937C211yesmaximal, characteristic, complemented
5C2×#63976C212yesmaximal, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#63970C212yesmaximal, complemented
8C2×D3×#217C211yesmaximal, characteristic, complemented
9C2×#63962C211yesmaximal, characteristic, complemented
10#10595230C2116yesmaximal, direct product factor
11C2×#63905C212yesmaximal, complemented
12C2×#63885C212yesmaximal, complemented
13C2×#5804—31nomaximal
14C2×#5589—31nomaximal
15C24×C3×D3C2211yescharacteristic
16C24×C3×D3C2211yescharacteristic, complemented
17C24×C3×D3C2211yescharacteristic, complemented
18C22×C32×D4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic, complemented
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic, complemented
22C22×C3×#67C2212yescomplemented
23C2×C3×D3×D4—28no—
24C2×C3×D3×D4C2218yescomplemented
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×#625—28no—
28C22×#625C2212yes—
29C22×#625C2212yescomplemented
30C22×#625C2212yescomplemented
31C22×#625C2218yescomplemented
32C22×D3×Dic3C2212yescomplemented
33C2×#3757C2211yescharacteristic, complemented
34C2×#3757C2212yescomplemented
35#64144C2218yescomplemented
36C2×#3750C2212yescomplemented
37C2×C3×#217C2211yescharacteristic, complemented
38C3×#937C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2212yescomplemented
40#63976C22116yescomplemented
41#63976C2218yescomplemented
42#63970C22116yescomplemented
43D3×#217C2218yescomplemented
44C2×Dic3⋊Dic3C2212yescomplemented
45#63962C2218yescomplemented
46C2×(C2×D3)⋊Dic3C2212yescomplemented
47C2×(C2×D3)⋊Dic3C2212yescomplemented
48C2×(C2×D3)⋊Dic3C2212yescomplemented
49#63905C22116yescomplemented
50#63885C22116yescomplemented
51C23×C3×D4—31no—
52C23×#67—31no—
53C23×#67—31no—
54C22×D3×D4D311yescharacteristic, complemented
55C2×C3×#120—31no—
56C2×#953—31no—
57C2×#953—32no—
58C22×#217—31no—
59#5804—316no—
60C2×#939—32no—
61C2×#939—32no—
62C2×#938—32no—
63C2×#937—32no—
64C2×#937—31no—
65C2×#937D311yescharacteristic, complemented
66C2×#935—31no—
67C2×#935—31no—
68C2×#935—31no—
69C2×#935—61no—
70C2×#929—32no—
71#5589—316no—
72C2×#886—31no—
73C2×#884—32no—
74C2×#883—32no—
75C2×D3×C22⋊C4—31no—
76C24×C32C2311yescharacteristic
77C24×C32C2311yescharacteristic
78C23×C3×D3—24no—
79C23×C3×D3—24no—
80C23×C3×D3—44no—
81C23×C3×D3—44no—
82C23×C3×D3—44no—
83C23×C3×D3D418yescomplemented
84C23×C3×D3C2312yes—
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2314yes—
89C23×C3×D3C2314yescomplemented
90C23×C3×D3C2314yescomplemented
91C2×C32×D4—24no—
92C2×C32×D4C2314yes—
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—24no—
95C22×C3⋊Dic3C2312yes—
96C22×C3⋊Dic3C2312yes—
97C22×C3⋊Dic3C2314yescomplemented
98C2×C3×#67—24no—
99C2×C3×#67—24no—
100C2×C3×#67—44no—
101C2×C3×#67C2314yes—
102C2×C3×#67C2314yescomplemented
103C2×C3×#67C2318yescomplemented
104C22×C3×Dic3C2312yes—
105C22×C3×Dic3C2311yescharacteristic
106C3×D3×D4—232no—
107C2×C3×D12—24no—
108C2×C3×D12C2314yescomplemented
109C2×C3×C4×D3—24no—
110C2×C3×C4×D3C2314yescomplemented
111C2×#625—28no—
112C2×#625—28no—
113C2×#625—232no—
114C2×#625—44no—
115C2×#625C2318yes—
116C2×#625C2318yescomplemented
117C2×#625C2318yescomplemented
118C2×D3×Dic3—44no—
119C2×D3×Dic3C2318yescomplemented
120#3757C2314yescomplemented
121#3757C2318yescomplemented
122#3750C2318yescomplemented
123C3×#217C2314yescomplemented
124C3×(C2×D3)⋊C4C2318yescomplemented
125Dic3⋊Dic3C2318yescomplemented
126(C2×D3)⋊Dic3C2318yescomplemented
127(C2×D3)⋊Dic3C2318yescomplemented
128(C2×D3)⋊Dic3C2318yescomplemented
129C2×#534—91noSylow
130C25×C3—31no—
131C25×C3—31no—
132C25×C3—31no—
133C24×D3C2×D311yescharacteristic
134C24×D3C2×D311yescharacteristic, complemented
135C24×D3C2×D311yescharacteristic, complemented
136C22×C3×D4—21no—
137C22×C3×D4—31no—
138C22×C3×D4—31no—
139C22×C3×D4—32no—
140C22×C3×D4—38no—
141C22×C3×D4—31no—
142C22×C3×D4—68no—
143C22×C3×D4C2×D311yescharacteristic
144C22×C3×D4C2×D311yescharacteristic
145C23×C3×C4—31no—
146C22×#67—32no—
147C22×#67—32no—
148C22×#67—32no—
149C22×#67—32no—
150C22×#67—38no—
151C22×#67—38no—
152C22×#67—32no—
153C22×#67—32no—
154C22×#67—68no—
155C22×#67—68no—
156C22×#67C2×D311yescharacteristic
157C22×#67C2×D311yescharacteristic, complemented
158C22×#67C2×D312yescomplemented
159C23×Dic3—31no—
160C23×Dic3—31no—
161C23×Dic3—32no—
162C23×Dic3—61no—
163C2×D3×D4—28no—
164C2×D3×D4C2×D318yescomplemented
165C22×D12C2×D311yescharacteristic, complemented
166C22×C4×D3—32no—
167C22×C4×D3C2×D311yescharacteristic, complemented
168C3×#120—38no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—32no—
171#953—38no—
172#953—316no—
173C2×#217—31no—
174C2×#217—32no—
175C2×#217—31no—
176C2×#217—32no—
177C2×#217—32no—
178C2×#217—32no—
179C2×#217—32no—
180C2×#217—38no—
181C2×#217—61no—
182C2×#217—62no—
183C2×#217C2×D311yescharacteristic, complemented
184#939—316no—
185#939—316no—
186#938—316no—
187#937—38no—
188#937—316no—
189#937C2×D318yescomplemented
190#935—38no—
191#935—38no—
192#935—38no—
193#935—68no—
194#929—316no—
195C2×(C2×D3)⋊C4—32no—
196C2×(C2×D3)⋊C4—32no—
197C2×(C2×D3)⋊C4—32no—
198C2×(C2×D3)⋊C4C2×D312yescomplemented
199C2×C4⋊Dic3—32no—
200C2×Dic3⋊C4—32no—
201C2×Dic3⋊C4—32no—
202C2×Dic3⋊C4—32no—
203C2×Dic3⋊C4—62no—
204#886—38no—
205#884—316no—
206#883—316no—
207D3×C22⋊C4—38no—
208C23×C32—24no—
209C23×C32—22no—
210C23×C32—24no—
211C23×C32C2×D414yes—
212C23×C32C2412yes—
213C23×C32C2412yes—
214C23×C32C2411yescharacteristic
215C22×C3×D3—24no—
216C22×C3×D3—24no—
217C22×C3×D3—24no—
218C22×C3×D3—22no—
219C22×C3×D3—28no—
220C22×C3×D3—24no—
221C22×C3×D3—24no—
222C22×C3×D3—24no—
223C22×C3×D3—28no—
224C22×C3×D3—416no—
225C22×C3×D3—48no—
226C22×C3×D3—48no—
227C22×C3×D3—48no—
228C22×C3×D3—416no—
229C22×C3×D3—416no—
230C22×C3×D3C2×D414yes—
231C22×C3×D3C2×D414yes—
232C22×C3×D3C2×D4116yescomplemented
233C22×C3×D3C2412yes—
234C22×C3×D3C2414yes—
235C22×C3×D3C2412yes—
236C22×C3×D3C2412yes—
237C32×D4—28no—
238C2×C32×C4—22no—
239C2×C32×C4C2412yes—
240C2×C3⋊Dic3—24no—
241C2×C3⋊Dic3—28no—
242C2×C3⋊Dic3—24no—
243C2×C3⋊Dic3C2414yes—
244C2×C3⋊Dic3C2414yes—
245C3×#67—28no—
246C3×#67—28no—
247C3×#67—48no—
248C2×C3×Dic3—22no—
249C2×C3×Dic3—24no—
250C2×C3×Dic3C2412yes—
251C2×C3×Dic3C2414yes—
252C3×D12—28no—
253C3×C4×D3—28no—
254#625—216no—
255#625—216no—
256#625—48no—
257D3×Dic3—48no—
258C23×D4—31no—
259C23×D4—91no—
260#534—916no—
261C2×#123—92no—
262C2×#123—91no—
263C2×#123—91no—
264C2×#121—92no—
265C2×#121—92no—
266C2×#120—31no—
267C2×#120—92no—
268C2×#120—91no—
269C22×C22⋊C4—91no—
270C24×C3—21no—
271C24×C3—21no—
272C24×C3—31no—
273C24×C3—31no—
274C24×C3—38no—
275C24×C3—34no—
276C24×C3—31no—
277C24×C3—32no—
278C24×C3—34no—
279C24×C3—34no—
280C24×C3—64no—
281C24×C3—64no—
282C24×C3—124no—
283C24×C3—124no—
284C24×C3—124no—
285C24×C3C22×D311yescharacteristic
286C24×C3C22×D311yescharacteristic
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C23×D3—24no—
290C23×D3—24no—
291C23×D3—44no—
292C23×D3—44no—
293C23×D3—44no—
294C23×D3#6718yescomplemented
295C23×D3C22×D311yescharacteristic
296C23×D3C22×D312yes—
297C23×D3C22×D311yescharacteristic
298C23×D3C22×D311yescharacteristic
299C23×D3C22×D314yes—
300C23×D3C22×D314yescomplemented
301C23×D3C22×D314yescomplemented
302C2×C3×D4—24no—
303C2×C3×D4—24no—
304C2×C3×D4—24no—
305C2×C3×D4—34no—
306C2×C3×D4—34no—
307C2×C3×D4—38no—
308C2×C3×D4—34no—
309C2×C3×D4—44no—
310C2×C3×D4—64no—
311C2×C3×D4—632no—
312C2×C3×D4—64no—
313C2×C3×D4—64no—
314C2×C3×D4—124no—
315C2×C3×D4C22×D314yes—
316C2×C3×D4C22×D314yes—
317C22×C3×C4—21no—
318C22×C3×C4—31no—
319C22×C3×C4—32no—
320C22×C3×C4—34no—
321C22×C3×C4—64no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C2×#67—24no—
325C2×#67—24no—
326C2×#67—38no—
327C2×#67—38no—
328C2×#67—38no—
329C2×#67—38no—
330C2×#67—38no—
331C2×#67—38no—
332C2×#67—44no—
333C2×#67—68no—
334C2×#67—68no—
335C2×#67—632no—
336C2×#67—68no—
337C2×#67—68no—
338C2×#67—632no—
339C2×#67—124no—
340C2×#67—124no—
341C2×#67C22×D314yes—
342C2×#67C22×D314yescomplemented
343C2×#67C22×D318yescomplemented
344C22×Dic3—34no—
345C22×Dic3—32no—
346C22×Dic3—32no—
347C22×Dic3—32no—
348C22×Dic3—32no—
349C22×Dic3—34no—
350C22×Dic3—38no—
351C22×Dic3—62no—
352C22×Dic3—62no—
353C22×Dic3—64no—
354C22×Dic3—64no—
355C22×Dic3—64no—
356C22×Dic3—124no—
357C22×Dic3—124no—
358C22×Dic3C22×D312yes—
359C22×Dic3C22×D311yescharacteristic
360D3×D4—232no—
361C2×D12—24no—
362C2×D12C22×D314yescomplemented
363C2×C4×D3—24no—
364C2×C4×D3—38no—
365C2×C4×D3—124no—
366C2×C4×D3C22×D314yescomplemented
367C3×C22⋊C4—34no—
368C3×C22⋊C4—38no—
369#217—34no—
370#217—38no—
371#217—34no—
372#217—38no—
373#217—38no—
374#217—38no—
375#217—38no—
376#217—64no—
377#217—68no—
378#217C22×D314yescomplemented
379(C2×D3)⋊C4—38no—
380(C2×D3)⋊C4—38no—
381(C2×D3)⋊C4—38no—
382(C2×D3)⋊C4C22×D318yescomplemented
383C4⋊Dic3—38no—
384Dic3⋊C4—38no—
385Dic3⋊C4—38no—
386Dic3⋊C4—38no—
387Dic3⋊C4—68no—
388C22×C32—28no—
389C22×C32—24no—
390C22×C32—22no—
391C22×C32—24no—
392C22×C32—44no—
393C22×C32C22×D414yes—
394C22×C32C22×D412yes—
395C22×C32H(5,𝔽2)14yes—
396C22×C32C2511yescharacteristic
397C2×C3×D3—28no—
398C2×C3×D3—28no—
399C2×C3×D3—24no—
400C2×C3×D3—24no—
401C2×C3×D3—24no—
402C2×C3×D3—22no—
403C2×C3×D3—24no—
404C2×C3×D3—24no—
405C2×C3×D3—24no—
406C2×C3×D3—416no—
407C2×C3×D3—416no—
408C2×C3×D3—416no—
409C2×C3×D3—44no—
410C2×C3×D3—48no—
411C2×C3×D3C22×D414yes—
412C2×C3×D3C22×D414yes—
413C32×C4—22no—
414C3⋊Dic3—24no—
415C3⋊Dic3—24no—
416C3×Dic3—22no—
417C3×Dic3—24no—
418C25—31no—
419C25—31no—
420C25—31no—
421C22×D4—31no—
422C22×D4—31no—
423C22×D4—32no—
424C22×D4—38no—
425C22×D4—31no—
426C22×D4—68no—
427C22×D4—92no—
428C22×D4—92no—
429C22×D4—98no—
430C22×D4—92no—
431C22×D4—188no—
432C22×D4D3211yescharacteristic
433C23×C4—31no—
434C23×C4—92no—
435C23×C4—91no—
436#123—916no—
437#123—98no—
438#123—98no—
439#121—916no—
440#121—916no—
441#120—38no—
442#120—916no—
443#120—98no—
444C2×C4⋊C4—92no—
445C2×C4⋊C4—92no—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—32no—
448C2×C22⋊C4—98no—
449C2×C22⋊C4—92no—
450C2×C22⋊C4—92no—
451C2×C22⋊C4—92no—
452C2×C22⋊C4—91no—
453C2×C22⋊C4—92no—
454C23×C3—24no—
455C23×C3—24no—
456C23×C3—22no—
457C23×C3—24no—
458C23×C3—24no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—21no—
463C23×C3—24no—
464C23×C3—34no—
465C23×C3—34no—
466C23×C3—32no—
467C23×C3—32no—
468C23×C3—316no—
469C23×C3—32no—
470C23×C3—34no—
471C23×C3—44no—
472C23×C3—42no—
473C23×C3—44no—
474C23×C3—68no—
475C23×C3—64no—
476C23×C3—64no—
477C23×C3—62no—
478C23×C3—64no—
479C23×C3—64no—
480C23×C3—64no—
481C23×C3—68no—
482C23×C3—64no—
483C23×C3—128no—
484C23×C3—128no—
485C23×C3—1216no—
486C23×C3—128no—
487C23×C3—1216no—
488C23×C3—1216no—
489C23×C3D3×D414yes—
490C23×C3C2×#6714yes—
491C23×C3C23×D312yes—
492C23×C3C23×D312yes—
493C23×C3C23×D312yes—
494C23×C3C23×D312yes—
495C23×C3C23×D311yescharacteristic
496C23×C3C23×D311yescharacteristic
497C22×D3—24no—
498C22×D3—24no—
499C22×D3—24no—
500C22×D3—28no—
501C22×D3—24no—
502C22×D3—24no—
503C22×D3—24no—
504C22×D3—22no—
505C22×D3—28no—
506C22×D3—416no—
507C22×D3—48no—
508C22×D3—48no—
509C22×D3—48no—
510C22×D3—416no—
511C22×D3—416no—
512C22×D3C2×#6714yes—
513C22×D3C2×#6714yes—
514C22×D3C2×#67116yescomplemented
515C22×D3C23×D312yes—
516C22×D3C23×D314yes—
517C22×D3C23×D312yes—
518C22×D3C23×D312yes—
519C3×D4—28no—
520C3×D4—28no—
521C3×D4—48no—
522C3×D4—68no—
523C3×D4—68no—
524C3×D4—68no—
525C3×D4—128no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—32no—
530C2×C3×C4—34no—
531C2×C3×C4—42no—
532C2×C3×C4—68no—
533C2×C3×C4—62no—
534C2×C3×C4—64no—
535C2×C3×C4C23×D312yes—
536C2×C3×C4C23×D312yes—
537#67—28no—
538#67—28no—
539#67—48no—
540#67—616no—
541#67—616no—
542#67—616no—
543#67—616no—
544#67—128no—
545#67—128no—
546C2×Dic3—24no—
547C2×Dic3—22no—
548C2×Dic3—34no—
549C2×Dic3—34no—
550C2×Dic3—34no—
551C2×Dic3—34no—
552C2×Dic3—64no—
553C2×Dic3—64no—
554C2×Dic3—68no—
555C2×Dic3—64no—
556C2×Dic3—64no—
557C2×Dic3—64no—
558C2×Dic3—68no—
559C2×Dic3—64no—
560C2×Dic3—124no—
561C2×Dic3—124no—
562C2×Dic3—128no—
563C2×Dic3—128no—
564C2×Dic3C23×D314yes—
565C2×Dic3C23×D312yes—
566D12—28no—
567C4×D3—28no—
568C4×D3—128no—
569C2×C32—24no—
570C2×C32—42no—
571C2×C32#53414yescomplemented
572C2×C32C23×D411yescharacteristic
573C2×C32C2×H(5,𝔽2)12yes—
574C3×D3—24no—
575C3×D3—24no—
576C3×D3—44no—
577C3×D3—42no—
578C24—31no—
579C24—31no—
580C24—34no—
581C24—38no—
582C24—32no—
583C24—31no—
584C24—34no—
585C24—34no—
586C24—64no—
587C24—64no—
588C24—124no—
589C24—124no—
590C24—124no—
591C24C2×D3211yescharacteristic
592C24C2×D3211yescharacteristic
593C2×D4—24no—
594C2×D4—34no—
595C2×D4—34no—
596C2×D4—38no—
597C2×D4—34no—
598C2×D4—64no—
599C2×D4—632no—
600C2×D4—64no—
601C2×D4—64no—
602C2×D4—98no—
603C2×D4—98no—
604C2×D4—98no—
605C2×D4—124no—
606C2×D4—188no—
607C2×D4—188no—
608C2×D4—1832no—
609C2×D4—364no—
610C2×D4C2×D3214yes—
611C22×C4—32no—
612C22×C4—31no—
613C22×C4—34no—
614C22×C4—64no—
615C22×C4—98no—
616C22×C4—94no—
617C22×C4—92no—
618C22×C4—92no—
619C22×C4—184no—
620C22×C4—364no—
621C22×C4C2×D3211yescharacteristic
622C4⋊C4—98no—
623C4⋊C4—98no—
624C22⋊C4—34no—
625C22⋊C4—38no—
626C22⋊C4—98no—
627C22⋊C4—98no—
628C22⋊C4—98no—
629C22⋊C4—94no—
630C22⋊C4—98no—
631C22×C3—24no—
632C22×C3—24no—
633C22×C3—28no—
634C22×C3—28no—
635C22×C3—22no—
636C22×C3—24no—
637C22×C3—24no—
638C22×C3—22no—
639C22×C3—24no—
640C22×C3—22no—
641C22×C3—24no—
642C22×C3—21no—
643C22×C3—34no—
644C22×C3—34no—
645C22×C3—44no—
646C22×C3—48no—
647C22×C3—42no—
648C22×C3—44no—
649C22×C3—44no—
650C22×C3—44no—
651C22×C3—64no—
652C22×C3—64no—
653C22×C3—68no—
654C22×C3—68no—
655C22×C3—62no—
656C22×C3—64no—
657C22×C3—64no—
658C22×C3—64no—
659C22×C3—64no—
660C22×C3—84no—
661C22×C3—1216no—
662C22×C3—1216no—
663C22×C3—1216no—
664C22×C3—128no—
665C22×C3—124no—
666C22×C3C2×D3×D414yes—
667C22×C3C2×D3×D412yes—
668C22×C3#100414yes—
669C22×C3#100414yes—
670C22×C3C22×#6714yes—
671C22×C3C22×#6712yes—
672C22×C3C24×D311yescharacteristic
673C22×C3C24×D311yescharacteristic
674C2×D3—24no—
675C2×D3—24no—
676C2×D3—28no—
677C2×D3—28no—
678C2×D3—24no—
679C2×D3—24no—
680C2×D3—24no—
681C2×D3—24no—
682C2×D3—22no—
683C2×D3—416no—
684C2×D3—416no—
685C2×D3—416no—
686C2×D3—44no—
687C2×D3—48no—
688C2×D3C22×#6714yes—
689C2×D3C22×#6714yes—
690C3×C4—22no—
691C3×C4—22no—
692C3×C4—42no—
693C3×C4—62no—
694C3×C4—64no—
695Dic3—24no—
696Dic3—22no—
697Dic3—64no—
698Dic3—64no—
699Dic3—64no—
700Dic3—64no—
701Dic3—124no—
702Dic3—124no—
703C32C2×#53411yescharacteristic, complemented, Sylow
704C23—24no—
705C23—24no—
706C23—22no—
707C23—34no—
708C23—34no—
709C23—32no—
710C23—32no—
711C23—316no—
712C23—34no—
713C23—32no—
714C23—68no—
715C23—64no—
716C23—64no—
717C23—64no—
718C23—64no—
719C23—64no—
720C23—62no—
721C23—68no—
722C23—64no—
723C23—128no—
724C23—128no—
725C23—1216no—
726C23—128no—
727C23—1216no—
728C23—1216no—
729C23D3×#6714yes—
730C23C22×D3212yes—
731C23C22×D3212yes—
732C23C22×D3211yescharacteristic
733D4—28no—
734D4—68no—
735D4—68no—
736D4—68no—
737D4—128no—
738D4—1816no—
739D4—1816no—
740D4—368no—
741C2×C4—22no—
742C2×C4—34no—
743C2×C4—32no—
744C2×C4—68no—
745C2×C4—64no—
746C2×C4—62no—
747C2×C4—94no—
748C2×C4—94no—
749C2×C4—184no—
750C2×C4—188no—
751C2×C4—184no—
752C2×C4—368no—
753C2×C4C22×D3212yes—
754C2×C3—24no—
755C2×C3—24no—
756C2×C3—22no—
757C2×C3—21no—
758C2×C3—24no—
759C2×C3—44no—
760C2×C3—42no—
761C2×C3—42no—
762C2×C3—64no—
763C2×C3—64no—
764C2×C3—82no—
765C2×C3—122no—
766C2×C3—124no—
767C2×C3#558914yescomplemented
768C2×C3#580414yescomplemented
769C2×C3C22×D3×D411yescharacteristic
770C2×C3C2×#100412yes—
771C2×C3C2×#100412yes—
772C2×C3C23×#6711yescharacteristic
773D3—24no—
774D3—24no—
775D3—44no—
776D3—42no—
777C22—24no—
778C22—28no—
779C22—24no—
780C22—22no—
781C22—34no—
782C22—34no—
783C22—44no—
784C22—64no—
785C22—64no—
786C22—68no—
787C22—68no—
788C22—64no—
789C22—64no—
790C22—64no—
791C22—62no—
792C22—64no—
793C22—1216no—
794C22—1216no—
795C22—1216no—
796C22—128no—
797C22—124no—
798C22#6431314yes—
799C22C2×D3×#6714yes—
800C22C2×D3×#6712yes—
801C22C23×D3211yescharacteristic
802C4—22no—
803C4—64no—
804C4—62no—
805C4—184no—
806C4—184no—
807C3—21no—
808C3C2×#558911yescharacteristic, complemented
809C3C2×#580411yescharacteristic, complemented
810C2—24no—
811C2—42no—
812C2—64no—
813C2—64no—
814C2—124no—
815C2—122no—
816C2#1059523014yesdirect product factor
817C2C2×#6431312yes—
818C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#534
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×D3×D4C2semidirect
2. C23×#625C2semidirect
3. C2×#64144C2semidirect
4. C2×C3×#937C2semidirect
5. C2×#63976C2semidirect
6. C2×#63976C2semidirect
7. C2×#63970C2semidirect
8. C2×D3×#217C2semidirect
9. C2×#63962C2semidirect
10. #10595230C2direct (N × H)
11. C2×#63905C2semidirect
12. C2×#63885C2semidirect
16. C24×C3×D3C22semidirect
17. C24×C3×D3C22semidirect
19. C23×C3⋊Dic3C22semidirect
21. C22×C3×#67C22semidirect
22. C22×C3×#67C22semidirect
24. C2×C3×D3×D4C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
29. C22×#625C22semidirect
30. C22×#625C22semidirect
31. C22×#625C22semidirect
32. C22×D3×Dic3C22semidirect
33. C2×#3757C22semidirect
34. C2×#3757C22semidirect
35. #64144C22semidirect
36. C2×#3750C22semidirect
37. C2×C3×#217C22semidirect
38. C3×#937C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. #63976C22semidirect
41. #63976C22semidirect
42. #63970C22semidirect
43. D3×#217C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
45. #63962C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. #63905C22semidirect
50. #63885C22semidirect
54. C22×D3×D4D3semidirect
65. C2×#937D3semidirect
83. C23×C3×D3D4semidirect
89. C23×C3×D3C23semidirect
90. C23×C3×D3C23semidirect
97. C22×C3⋊Dic3C23semidirect
102. C2×C3×#67C23semidirect
103. C2×C3×#67C23semidirect
108. C2×C3×D12C23semidirect
110. C2×C3×C4×D3C23semidirect
116. C2×#625C23semidirect
117. C2×#625C23semidirect
119. C2×D3×Dic3C23semidirect
120. #3757C23semidirect
121. #3757C23semidirect
122. #3750C23semidirect
123. C3×#217C23semidirect
124. C3×(C2×D3)⋊C4C23semidirect
125. Dic3⋊Dic3C23semidirect
126. (C2×D3)⋊Dic3C23semidirect
127. (C2×D3)⋊Dic3C23semidirect
128. (C2×D3)⋊Dic3C23semidirect
134. C24×D3C2×D3semidirect
135. C24×D3C2×D3semidirect
157. C22×#67C2×D3semidirect
158. C22×#67C2×D3semidirect
164. C2×D3×D4C2×D3semidirect
165. C22×D12C2×D3semidirect
167. C22×C4×D3C2×D3semidirect
183. C2×#217C2×D3semidirect
189. #937C2×D3semidirect
198. C2×(C2×D3)⋊C4C2×D3semidirect
232. C22×C3×D3C2×D4semidirect
294. C23×D3#67semidirect
300. C23×D3C22×D3semidirect
301. C23×D3C22×D3semidirect
342. C2×#67C22×D3semidirect
343. C2×#67C22×D3semidirect
362. C2×D12C22×D3semidirect
366. C2×C4×D3C22×D3semidirect
378. #217C22×D3semidirect
382. (C2×D3)⋊C4C22×D3semidirect
514. C22×D3C2×#67semidirect
571. C2×C32#534semidirect
703. C32C2×#534semidirect
767. C2×C3#5589semidirect
768. C2×C3#5804semidirect
808. C3C2×#5589semidirect
809. C3C2×#5804semidirect
816. C2#10595230direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C23×#6252
C2×#641442
C2×C3×#9372
C2×#639762
C2×#639702
C2×D3×#2172
C2×#639622
#105952302
C2×#639052
C2×#638852
C2×#58043
C2×#55893