Finite Group Databasebeta

← C2×#82686 #11429930

Subgroups — C2×#82686 #11429930

Order 768.

3934 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C22×#935C211yesmaximal, characteristic, complemented
3C22×#939C211yesmaximal, characteristic, complemented
4C22×#929C211yesmaximal, characteristic, complemented
5C2×#5223C211yesmaximal, characteristic, complemented
6C2×#5223C211yesmaximal, characteristic, complemented
7C2×#5222C211yesmaximal, characteristic, complemented
8C2×#5221C211yesmaximal, characteristic, complemented
9C2×#5210C211yesmaximal, characteristic, complemented
10#82686C2116yesmaximal, direct product factor
11C2×#4994C211yesmaximal, characteristic, complemented
12C2×#4976C211yesmaximal, characteristic, complemented
13C2×#4959C211yesmaximal, characteristic, complemented
14C2×#4948C211yesmaximal, characteristic, complemented
15C2×#4957C211yesmaximal, characteristic, complemented
16C2×#4946C211yesmaximal, characteristic, complemented
17C2×#2682—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×#67C2211yescharacteristic
25C24×Dic3C2211yescharacteristic
26C2×C3×#121—28no—
27C2×C3×#121C2218yescomplemented
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C2×#939—28no—
40C2×#939C2218yescomplemented
41C2×#935—28no—
42C2×#935C2218yescomplemented
43C2×#929—28no—
44C2×#929C2218yescomplemented
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C2211yescharacteristic
47C22×(C2×D3)⋊C4C2211yescharacteristic
48C22×(C2×D3)⋊C4C2211yescharacteristic
49C22×C4⋊Dic3C2211yescharacteristic
50C22×Dic3⋊C4C2211yescharacteristic
51C22×Dic3⋊C4C2211yescharacteristic
52C22×Dic3⋊C4C2211yescharacteristic
53C22×Dic3⋊C4C2211yescharacteristic
54C22×Dic3⋊C4C2211yescharacteristic
55C22×Dic3⋊C4C2211yescharacteristic
56C22×C4×Dic3C2211yescharacteristic
57#5223C2218yescomplemented
58#5223C2218yescomplemented
59#5222C2218yescomplemented
60#5221C2218yescomplemented
61#5210C2218yescomplemented
62C2×C3⋊#95C2211yescharacteristic
63C2×C3⋊#95C2211yescharacteristic
64C2×C3⋊#95C2211yescharacteristic
65C2×C3⋊#95C2211yescharacteristic
66#4994C2218yescomplemented
67#4976C2218yescomplemented
68#4959C2218yescomplemented
69#4957C2218yescomplemented
70#4948C2218yescomplemented
71#4946C2218yescomplemented
72C22×#123—31no—
73C22×#123—31no—
74C22×#121—31no—
75C22×#121D311yescharacteristic, complemented
76#2682—316no—
77C2×#396—31no—
78C2×#396—31no—
79C2×#394—31no—
80C2×#394—31no—
81C2×#392—31no—
82C2×#392—31no—
83C2×#390—31no—
84C2×#390—31no—
85C2×#389—31no—
86C2×#385—31no—
87C2×#385—31no—
88C25×C3C2311yescharacteristic
89C25×C3C2311yescharacteristic
90C25×C3C2311yescharacteristic
91C24×D3C2311yescharacteristic
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4—24no—
95C22×C3×D4—42no—
96C22×C3×D4—42no—
97C22×C3×D4—42no—
98C22×C3×D4—42no—
99C22×C3×D4—42no—
100C22×C3×D4D418yescomplemented
101C22×C3×D4C2314yes—
102C22×C3×D4C2314yes—
103C22×C3×D4C2314yes—
104C23×C3×C4—24no—
105C23×C3×C4—24no—
106C23×C3×C4—42no—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2314yes—
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C22×#67—24no—
113C22×#67—24no—
114C22×#67—24no—
115C22×#67—24no—
116C22×#67—42no—
117C22×#67—42no—
118C22×#67—42no—
119C22×#67—42no—
120C22×#67—42no—
121C22×#67C2314yes—
122C22×#67C2314yes—
123C22×#67C2314yes—
124C23×Dic3—24no—
125C23×Dic3—24no—
126C23×Dic3—42no—
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2311yescharacteristic
129C23×Dic3C2311yescharacteristic
130C23×Dic3C2311yescharacteristic
131C23×Dic3C2314yes—
132C23×Dic3C2311yescharacteristic
133C23×Dic3C2311yescharacteristic
134C23×Dic3C2311yescharacteristic
135C3×#121—232no—
136C2×C3×C4⋊C4—24no—
137C2×C3×C4⋊C4C2314yes—
138C2×C3×C22⋊C4—24no—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4C2314yes—
141C2×C3×C22⋊C4C2314yes—
142C2×#217—24no—
143C2×#217—24no—
144C2×#217—24no—
145C2×#217—24no—
146C2×#217—24no—
147C2×#217—24no—
148C2×#217—24no—
149C2×#217—42no—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×#217C2314yes—
153C2×#217C2314yes—
154C2×#217C2314yes—
155C2×#217C2314yes—
156C2×#217C2314yes—
157C2×#217C2314yes—
158#939—232no—
159#935—232no—
160#929—232no—
161C2×(C2×D3)⋊C4—24no—
162C2×(C2×D3)⋊C4—24no—
163C2×(C2×D3)⋊C4—24no—
164C2×(C2×D3)⋊C4—42no—
165C2×(C2×D3)⋊C4C2314yes—
166C2×(C2×D3)⋊C4C2314yes—
167C2×(C2×D3)⋊C4C2314yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×C4⋊Dic3—42no—
170C2×C4⋊Dic3C2314yes—
171C2×Dic3⋊C4—24no—
172C2×Dic3⋊C4—24no—
173C2×Dic3⋊C4—24no—
174C2×Dic3⋊C4—42no—
175C2×Dic3⋊C4—42no—
176C2×Dic3⋊C4D418yescomplemented
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179C2×Dic3⋊C4C2314yes—
180C2×Dic3⋊C4C2314yes—
181C2×Dic3⋊C4C2314yes—
182C2×Dic3⋊C4C2314yes—
183C2×C4×Dic3—42no—
184C2×C4×Dic3C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—31no—
192C23×D4C2×D311yescharacteristic
193C23×D4C2×D311yescharacteristic
194C23×D4C2×D311yescharacteristic
195C24×C4—31no—
196C24×C4C2×D311yescharacteristic
197C2×#123—38no—
198C2×#123—38no—
199C2×#123—68no—
200C2×#123—68no—
201C2×#121—28no—
202C2×#121—38no—
203C2×#121—68no—
204C2×#121C2×D318yescomplemented
205C22×C4⋊C4—31no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4—31no—
209C22×C4⋊C4—31no—
210C22×C4⋊C4—31no—
211C22×C4⋊C4—31no—
212C22×C4⋊C4C2×D311yescharacteristic
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C22⋊C4—31no—
224C22×C22⋊C4—31no—
225C22×C22⋊C4C2×D311yescharacteristic
226C22×C22⋊C4C2×D311yescharacteristic
227C22×C42—31no—
228#396—38no—
229#396—38no—
230#394—38no—
231#394—38no—
232#392—38no—
233#392—38no—
234#390—38no—
235#390—38no—
236#389—38no—
237#385—38no—
238#385—38no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95—31no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—22no—
253C24×C3—22no—
254C24×C3—22no—
255C24×C3—22no—
256C24×C3—22no—
257C24×C3—22no—
258C24×C3—22no—
259C24×C3—22no—
260C24×C3—22no—
261C24×C3—22no—
262C24×C3C2×D414yes—
263C24×C3C2×D414yes—
264C24×C3C2412yes—
265C24×C3C2412yes—
266C24×C3C2412yes—
267C24×C3C2411yescharacteristic
268C23×D3—22no—
269C23×D3—22no—
270C23×D3—22no—
271C23×D3—22no—
272C23×D3—22no—
273C23×D3—22no—
274C23×D3—22no—
275C23×D3C2412yes—
276C2×C3×D4—28no—
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—416no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
284C2×C3×D4—44no—
285C2×C3×D4—416no—
286C2×C3×D4—416no—
287C2×C3×D4C2×D4116yescomplemented
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—28no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4—28no—
300C22×C3×C4—44no—
301C22×C3×C4—416no—
302C22×C3×C4C2×D414yes—
303C22×C3×C4C2×D414yes—
304C22×C3×C4C2412yes—
305C22×C3×C4C2412yes—
306C22×C3×C4C2412yes—
307C22×C3×C4C2412yes—
308C2×#67—28no—
309C2×#67—28no—
310C2×#67—28no—
311C2×#67—28no—
312C2×#67—44no—
313C2×#67—44no—
314C2×#67—44no—
315C2×#67—44no—
316C2×#67—44no—
317C2×#67—416no—
318C2×#67—416no—
319C2×#67—416no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3—22no—
328C22×Dic3—22no—
329C22×Dic3—22no—
330C22×Dic3—22no—
331C22×Dic3—28no—
332C22×Dic3—22no—
333C22×Dic3—22no—
334C22×Dic3—22no—
335C22×Dic3—22no—
336C22×Dic3—22no—
337C22×Dic3—22no—
338C22×Dic3—22no—
339C22×Dic3—28no—
340C22×Dic3—44no—
341C22×Dic3—416no—
342C22×Dic3C2×D414yes—
343C22×Dic3C2×D414yes—
344C22×Dic3#4114yes—
345C22×Dic3C2412yes—
346C22×Dic3C2412yes—
347C22×Dic3C2412yes—
348C22×Dic3C2412yes—
349C22×Dic3C2412yes—
350C22×Dic3C2412yes—
351C22×Dic3C2412yes—
352C3×C4⋊C4—28no—
353C3×C22⋊C4—28no—
354C3×C22⋊C4—28no—
355#217—28no—
356#217—28no—
357#217—28no—
358#217—28no—
359#217—28no—
360#217—28no—
361#217—28no—
362#217—44no—
363(C2×D3)⋊C4—28no—
364(C2×D3)⋊C4—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—44no—
367C4⋊Dic3—44no—
368Dic3⋊C4—28no—
369Dic3⋊C4—28no—
370Dic3⋊C4—28no—
371Dic3⋊C4—44no—
372Dic3⋊C4—44no—
373Dic3⋊C4C2×D4116yescomplemented
374C4×Dic3—44no—
375C25—31no—
376C25C22×D311yescharacteristic
377C25C22×D311yescharacteristic
378C25C22×D311yescharacteristic
379C22×D4—24no—
380C22×D4—24no—
381C22×D4—24no—
382C22×D4—34no—
383C22×D4—34no—
384C22×D4—34no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4—42no—
390C22×D4—64no—
391C22×D4—64no—
392C22×D4—64no—
393C22×D4—64no—
394C22×D4—122no—
395C22×D4—122no—
396C22×D4—122no—
397C22×D4—122no—
398C22×D4—122no—
399C22×D4#6718yescomplemented
400C22×D4C22×D314yes—
401C22×D4C22×D314yes—
402C22×D4C22×D314yes—
403C23×C4—24no—
404C23×C4—24no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—34no—
413C23×C4—42no—
414C23×C4—64no—
415C23×C4—64no—
416C23×C4—122no—
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D314yes—
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422#123—632no—
423#123—632no—
424#121—232no—
425#121—632no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—38no—
428C2×C4⋊C4—34no—
429C2×C4⋊C4—34no—
430C2×C4⋊C4—34no—
431C2×C4⋊C4—34no—
432C2×C4⋊C4—34no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—64no—
436C2×C4⋊C4—64no—
437C2×C4⋊C4—64no—
438C2×C4⋊C4—122no—
439C2×C4⋊C4—122no—
440C2×C4⋊C4—122no—
441C2×C4⋊C4C22×D314yes—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4—34no—
450C2×C22⋊C4—34no—
451C2×C22⋊C4—34no—
452C2×C22⋊C4—34no—
453C2×C22⋊C4—34no—
454C2×C22⋊C4—34no—
455C2×C22⋊C4—34no—
456C2×C22⋊C4—64no—
457C2×C22⋊C4—64no—
458C2×C22⋊C4—64no—
459C2×C22⋊C4—64no—
460C2×C22⋊C4—64no—
461C2×C22⋊C4—64no—
462C2×C22⋊C4—64no—
463C2×C22⋊C4—64no—
464C2×C22⋊C4—64no—
465C2×C22⋊C4—64no—
466C2×C22⋊C4—122no—
467C2×C22⋊C4—122no—
468C2×C22⋊C4C22×D314yes—
469C2×C22⋊C4C22×D314yes—
470C2×C42—34no—
471C2×C42—122no—
472#95—34no—
473#95—34no—
474#95—34no—
475#95—34no—
476C23×C3—28no—
477C23×C3—28no—
478C23×C3—28no—
479C23×C3—28no—
480C23×C3—28no—
481C23×C3—28no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—44no—
502C23×C3—44no—
503C23×C3—44no—
504C23×C3—44no—
505C23×C3—44no—
506C23×C3—44no—
507C23×C3—44no—
508C23×C3—44no—
509C23×C3—44no—
510C23×C3—44no—
511C23×C3—44no—
512C23×C3—44no—
513C23×C3—44no—
514C23×C3—44no—
515C23×C3—44no—
516C23×C3C22×D412yes—
517C23×C3C22×D414yes—
518C23×C3C22×D414yes—
519C23×C3C22×D412yes—
520C23×C3C2×#4112yes—
521C23×C3H(5,𝔽2)12yes—
522C23×C3H(5,𝔽2)12yes—
523C23×C3H(5,𝔽2)12yes—
524C23×C32−1+412yes—
525C23×C3C2511yescharacteristic
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—44no—
534C22×D3—44no—
535C22×D3—44no—
536C22×D3—44no—
537C22×D3—44no—
538C22×D3—44no—
539C22×D3—44no—
540C3×D4—416no—
541C3×D4—416no—
542C3×D4—416no—
543C2×C3×C4—28no—
544C2×C3×C4—28no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—416no—
556C2×C3×C4—44no—
557C2×C3×C4—44no—
558C2×C3×C4C22×D414yes—
559C2×C3×C4C22×D414yes—
560#67—416no—
561#67—416no—
562#67—416no—
563C2×Dic3—28no—
564C2×Dic3—28no—
565C2×Dic3—28no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—416no—
585C2×Dic3—44no—
586C2×Dic3—44no—
587C2×Dic3—44no—
588C2×Dic3—44no—
589C2×Dic3C22×D414yes—
590C2×Dic3C22×D414yes—
591C2×Dic3C2×#4114yes—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—32no—
612C24—62no—
613C24—62no—
614C24—62no—
615C24—62no—
616C24—62no—
617C24—62no—
618C24—62no—
619C24C2×#6714yes—
620C24C2×#6714yes—
621C24C23×D312yes—
622C24C23×D312yes—
623C24C23×D312yes—
624C24C23×D311yescharacteristic
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—416no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—416no—
635C2×D4—416no—
636C2×D4—68no—
637C2×D4—68no—
638C2×D4—68no—
639C2×D4—68no—
640C2×D4—124no—
641C2×D4—124no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C2×D4—1216no—
646C2×D4—1216no—
647C2×D4—1216no—
648C2×D4C2×#67116yescomplemented
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—34no—
662C22×C4—34no—
663C22×C4—34no—
664C22×C4—32no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—44no—
672C22×C4—416no—
673C22×C4—68no—
674C22×C4—62no—
675C22×C4—62no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—68no—
693C22×C4—124no—
694C22×C4—1216no—
695C22×C4D3×D414yes—
696C22×C4C2×#6714yes—
697C22×C4C23×D312yes—
698C22×C4C23×D312yes—
699C22×C4C23×D312yes—
700C22×C4C23×D312yes—
701C4⋊C4—28no—
702C4⋊C4—316no—
703C4⋊C4—68no—
704C4⋊C4—68no—
705C4⋊C4—68no—
706C4⋊C4—124no—
707C4⋊C4—124no—
708C4⋊C4—124no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—68no—
712C22⋊C4—68no—
713C22⋊C4—68no—
714C22⋊C4—68no—
715C22⋊C4—68no—
716C22⋊C4—68no—
717C22⋊C4—68no—
718C22⋊C4—68no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—124no—
722C22⋊C4—124no—
723C42—124no—
724C22×C3—24no—
725C22×C3—24no—
726C22×C3—24no—
727C22×C3—24no—
728C22×C3—24no—
729C22×C3—24no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—416no—
733C22×C3—416no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—42no—
746C22×C3—42no—
747C22×C3—88no—
748C22×C3#53414yes—
749C22×C3#53714yes—
750C22×C3#53814yes—
751C22×C3D4214yes—
752C22×C3#54714yes—
753C22×C3#55014yes—
754C22×C3#56214yes—
755C22×C3C23×D411yescharacteristic
756C22×C3C23×D411yescharacteristic
757C22×C3C22×#4111yescharacteristic
758C22×C3C2×H(5,𝔽2)11yescharacteristic
759C22×C3C2×H(5,𝔽2)11yescharacteristic
760C22×C3C2×H(5,𝔽2)11yescharacteristic
761C22×C3C2×2−1+411yescharacteristic
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—42no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—88no—
770C3×C4—24no—
771C3×C4—24no—
772C3×C4—42no—
773C3×C4—42no—
774Dic3—24no—
775Dic3—24no—
776Dic3—24no—
777Dic3—42no—
778Dic3—42no—
779Dic3—42no—
780Dic3—42no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—28no—
794C23—28no—
795C23—28no—
796C23—28no—
797C23—28no—
798C23—28no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—62no—
822C23—62no—
823C23—62no—
824C23—62no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—124no—
829C23—124no—
830C23—124no—
831C23—124no—
832C23—124no—
833C23—124no—
834C23—124no—
835C23C2×D3×D412yes—
836C23#100412yes—
837C23#100412yes—
838C23#100412yes—
839C23D3×#4112yes—
840C23#101012yes—
841C23C22×#6714yes—
842C23C22×#6714yes—
843C23C22×#6712yes—
844C23C24×D311yescharacteristic
845D4—416no—
846D4—416no—
847D4—416no—
848D4—1216no—
849D4—1216no—
850D4—1216no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—28no—
856C2×C4—28no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—34no—
864C2×C4—34no—
865C2×C4—34no—
866C2×C4—416no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—68no—
876C2×C4—68no—
877C2×C4—68no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—1216no—
891C2×C4—124no—
892C2×C4—124no—
893C2×C4—124no—
894C2×C4—124no—
895C2×C4C2×D3×D414yes—
896C2×C4C22×#6714yes—
897C2×C3—44no—
898C2×C3—44no—
899C2×C3—82no—
900C2×C3#268218yescomplemented
901C2×C3C2×#53411yescharacteristic
902C2×C3C2×#53711yescharacteristic
903C2×C3C2×#53811yescharacteristic
904C2×C3C2×D4211yescharacteristic
905C2×C3C2×#54711yescharacteristic
906C2×C3C2×#55011yescharacteristic
907C2×C3C2×#56211yescharacteristic
908D3—82no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—416no—
924C22—416no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—88no—
933C22—122no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22—122no—
938C22—122no—
939C22—122no—
940C22—248no—
941C22#559914yes—
942C22#560814yes—
943C22#561314yes—
944C22#562114yes—
945C22D4×#6714yes—
946C22#580414yes—
947C22#582414yes—
948C22C22×D3×D411yescharacteristic
949C22C2×#100411yescharacteristic
950C22C2×#100411yescharacteristic
951C22C2×#100411yescharacteristic
952C22C2×D3×#4111yescharacteristic
953C22C2×#101011yescharacteristic
954C22C23×#6711yescharacteristic
955C4—24no—
956C4—24no—
957C4—42no—
958C4—42no—
959C4—64no—
960C4—64no—
961C4—64no—
962C4—122no—
963C4—122no—
964C4—122no—
965C4—122no—
966C3C2×#268211yescharacteristic, complemented, Sylow
967C2—44no—
968C2—44no—
969C2—82no—
970C2—242no—
971C2#8268618yesdirect product factor
972C2C2×#559911yescharacteristic
973C2C2×#560811yescharacteristic
974C2C2×#561311yescharacteristic
975C2C2×#562111yescharacteristic
976C2C2×#580411yescharacteristic
977C2C2×D4×#6711yescharacteristic
978C2C2×#582411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#121C2
socleC24×C3C24
hypercenterC22×#121D3
hypocenterC3C2×#2682
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C22×#935C2semidirect
3. C22×#939C2semidirect
4. C22×#929C2semidirect
5. C2×#5223C2semidirect
6. C2×#5223C2semidirect
7. C2×#5222C2semidirect
8. C2×#5221C2semidirect
9. C2×#5210C2semidirect
10. #82686C2direct (N × H)
11. C2×#4994C2semidirect
12. C2×#4976C2semidirect
13. C2×#4959C2semidirect
14. C2×#4948C2semidirect
15. C2×#4957C2semidirect
16. C2×#4946C2semidirect
27. C2×C3×#121C22semidirect
40. C2×#939C22semidirect
42. C2×#935C22semidirect
44. C2×#929C22semidirect
57. #5223C22semidirect
58. #5223C22semidirect
59. #5222C22semidirect
60. #5221C22semidirect
61. #5210C22semidirect
66. #4994C22semidirect
67. #4976C22semidirect
68. #4959C22semidirect
69. #4957C22semidirect
70. #4948C22semidirect
71. #4946C22semidirect
75. C22×#121D3semidirect
100. C22×C3×D4D4semidirect
176. C2×Dic3⋊C4D4semidirect
204. C2×#121C2×D3semidirect
287. C2×C3×D4C2×D4semidirect
373. Dic3⋊C4C2×D4semidirect
399. C22×D4#67semidirect
648. C2×D4C2×#67semidirect
900. C2×C3#2682semidirect
966. C3C2×#2682semidirect
971. C2#82686direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C22×#9352
C22×#9392
C22×#9292
C2×#52232
C2×#52222
C2×#52212
C2×#52102
#826862
C2×#49942
C2×#49762
C2×#49592
C2×#49482
C2×#49572
C2×#49462
C2×#26823