Finite Group Databasebeta

← C2×#76716 #11429936

Subgroups — C2×#76716 #11429936

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×#938C211yesmaximal, characteristic, complemented
2C22×#935C211yesmaximal, characteristic, complemented
3C22×#939C211yesmaximal, characteristic, complemented
4C22×#883C211yesmaximal, characteristic, complemented
5C2×C3×#392C211yesmaximal, characteristic, complemented
6C2×#5223C211yesmaximal, characteristic, complemented
7C2×#5222C211yesmaximal, characteristic, complemented
8C2×#5221C211yesmaximal, characteristic, complemented
9C2×#4959C211yesmaximal, characteristic, complemented
10C2×#4948C211yesmaximal, characteristic, complemented
11C2×#4948C211yesmaximal, characteristic, complemented
12C2×#4957C211yesmaximal, characteristic, complemented
13C2×#4950C211yesmaximal, characteristic, complemented
14#76716C2116yesmaximal, direct product factor
15C2×#4668C211yesmaximal, characteristic, complemented
16C2×#4647C211yesmaximal, characteristic, complemented
17C2×#2682—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C24×Dic3C2211yescharacteristic
25C23×C4×D3C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C2×#939—28no—
38C2×#939C2218yescomplemented
39C2×#938—28no—
40C2×#938C2218yescomplemented
41C2×#935—28no—
42C2×#935C2218yescomplemented
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×C4⋊Dic3C2211yescharacteristic
47C22×C4⋊Dic3C2211yescharacteristic
48C22×C4⋊Dic3C2211yescharacteristic
49C22×Dic3⋊C4C2211yescharacteristic
50C22×Dic3⋊C4C2211yescharacteristic
51C22×Dic3⋊C4C2211yescharacteristic
52C22×Dic3⋊C4C2211yescharacteristic
53C22×Dic3⋊C4C2211yescharacteristic
54C22×C4×Dic3C2211yescharacteristic
55C2×#883—28no—
56C2×#883C2218yescomplemented
57C3×#392C2218yescomplemented
58C2×C3×#95C2211yescharacteristic
59#5223C2218yescomplemented
60#5222C2218yescomplemented
61#5221C2218yescomplemented
62C2×C3⋊#95C2211yescharacteristic
63C2×C3⋊#95C2211yescharacteristic
64C2×C3⋊#95C2211yescharacteristic
65#4959C2218yescomplemented
66#4957C2218yescomplemented
67#4950C2218yescomplemented
68#4948C2218yescomplemented
69#4948C2218yescomplemented
70#4668C2218yescomplemented
71#4647C2218yescomplemented
72C22×#123—31no—
73C22×#123—31no—
74C22×#121—31no—
75C22×#121—31no—
76#2682—316no—
77C2×#396—31no—
78C2×#396—31no—
79C2×#394—31no—
80C2×#394—31no—
81C2×#392—31no—
82C2×#392D311yescharacteristic, complemented
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—24no—
96C22×C3×D4—42no—
97C22×C3×D4—42no—
98C22×C3×D4—42no—
99C22×C3×D4—42no—
100C22×C3×D4—42no—
101C22×C3×D4C2314yes—
102C22×C3×D4C2314yes—
103C22×C3×D4C2314yes—
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67—24no—
109C22×#67—24no—
110C22×#67—24no—
111C22×#67—42no—
112C22×#67—42no—
113C22×#67—42no—
114C22×#67—42no—
115C22×#67—42no—
116C22×#67D418yescomplemented
117C22×#67C2314yes—
118C22×#67C2314yes—
119C22×#67C2314yes—
120C23×Dic3—24no—
121C23×Dic3—24no—
122C23×Dic3—42no—
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C23×Dic3C2314yes—
128C23×Dic3C2311yescharacteristic
129C23×Dic3C2311yescharacteristic
130C23×Dic3C2311yescharacteristic
131C22×C4×D3—24no—
132C22×C4×D3—24no—
133C22×C4×D3—42no—
134C22×C4×D3C2314yes—
135C2×C3×C22⋊C4—24no—
136C2×C3×C22⋊C4—24no—
137C2×C3×C22⋊C4—42no—
138C2×C3×C22⋊C4C2314yes—
139C2×C3×C22⋊C4C2314yes—
140C2×C3×C22⋊C4C2314yes—
141C2×#217—24no—
142C2×#217—24no—
143C2×#217—24no—
144C2×#217—24no—
145C2×#217—24no—
146C2×#217—24no—
147C2×#217—24no—
148C2×#217—42no—
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×#217C2314yes—
153C2×#217C2314yes—
154C2×#217C2314yes—
155C2×#217C2314yes—
156C2×#217C2314yes—
157#939—232no—
158#938—232no—
159#935—232no—
160C2×(C2×D3)⋊C4—24no—
161C2×(C2×D3)⋊C4—24no—
162C2×(C2×D3)⋊C4—24no—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×(C2×D3)⋊C4C2314yes—
166C2×C4⋊Dic3—24no—
167C2×C4⋊Dic3—24no—
168C2×C4⋊Dic3—42no—
169C2×C4⋊Dic3C2314yes—
170C2×C4⋊Dic3C2314yes—
171C2×C4⋊Dic3C2314yes—
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×C4×Dic3—42no—
183C2×C4×Dic3C2314yes—
184#883—232no—
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×C4—31no—
197C2×#123—38no—
198C2×#123—38no—
199C2×#123—68no—
200C2×#123—68no—
201C2×#121—38no—
202C2×#121—38no—
203C2×#121—68no—
204C2×#121—68no—
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⋊C4—31no—
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⋊C4C2×D311yescharacteristic
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#392C2×D318yescomplemented
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×#95C2×D311yescharacteristic
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×C3—22no—
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×D3C2×D414yes—
275C23×D3C2412yes—
276C2×C3×D4—28no—
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—28no—
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×D4—416no—
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—22no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4C2×D414yes—
299C22×C3×C4#4114yes—
300C22×C3×C4C2412yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2412yes—
303C22×C3×C4C2412yes—
304C2×#67—28no—
305C2×#67—28no—
306C2×#67—28no—
307C2×#67—416no—
308C2×#67—44no—
309C2×#67—44no—
310C2×#67—44no—
311C2×#67—44no—
312C2×#67—44no—
313C2×#67—416no—
314C2×#67—416no—
315C2×#67C2×D4116yescomplemented
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3—28no—
328C22×Dic3—22no—
329C22×Dic3—22no—
330C22×Dic3—22no—
331C22×Dic3—22no—
332C22×Dic3—22no—
333C22×Dic3—22no—
334C22×Dic3—22no—
335C22×Dic3—28no—
336C22×Dic3—44no—
337C22×Dic3—416no—
338C22×Dic3C2×D414yes—
339C22×Dic3C2×D414yes—
340C22×Dic3C2×D414yes—
341C22×Dic3C2412yes—
342C22×Dic3C2412yes—
343C22×Dic3C2412yes—
344C22×Dic3C2412yes—
345C22×Dic3C2412yes—
346C22×Dic3C2412yes—
347C22×Dic3C2412yes—
348C2×C4×D3—28no—
349C2×C4×D3—28no—
350C2×C4×D3—44no—
351C2×C4×D3—416no—
352C3×C22⋊C4—28no—
353C3×C22⋊C4—28no—
354C3×C22⋊C4—44no—
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—
366C4⋊Dic3—28no—
367C4⋊Dic3—28no—
368C4⋊Dic3—44no—
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—24no—
383C22×D4—38no—
384C22×D4—34no—
385C22×D4—34no—
386C22×D4—34no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4—42no—
390C22×D4—42no—
391C22×D4—42no—
392C22×D4—64no—
393C22×D4—64no—
394C22×D4—64no—
395C22×D4—122no—
396C22×D4—122no—
397C22×D4—122no—
398C22×D4—122no—
399C22×D4—122no—
400C22×D4C22×D314yes—
401C22×D4C22×D314yes—
402C22×D4C22×D314yes—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—34no—
411C23×C4—34no—
412C23×C4—64no—
413C23×C4—64no—
414C23×C4—64no—
415C23×C4—64no—
416C23×C4—122no—
417C23×C4—122no—
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422#123—632no—
423#123—632no—
424#121—632no—
425#121—632no—
426C2×C4⋊C4—38no—
427C2×C4⋊C4—34no—
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—64no—
439C2×C4⋊C4—122no—
440C2×C4⋊C4—122no—
441C2×C4⋊C4—122no—
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—42no—
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⋊C4C22×D314yes—
468C2×C22⋊C4C22×D314yes—
469C2×C22⋊C4C22×D314yes—
470C2×C42—34no—
471C2×C42—122no—
472#95—34no—
473#95—34no—
474#95—34no—
475#95C22×D314yes—
476C23×C3—28no—
477C23×C3—28no—
478C23×C3—28no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
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—44no—
500C23×C3—44no—
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×C3—44no—
517C23×C3C22×D414yes—
518C23×C3C22×D412yes—
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—28no—
527C22×D3—28no—
528C22×D3—28no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—44no—
536C22×D3—44no—
537C22×D3—44no—
538C22×D3—44no—
539C22×D3C22×D414yes—
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—44no—
556C2×C3×C4—44no—
557C2×C3×C4C22×D414yes—
558C2×C3×C4C2×#4114yes—
559#67—416no—
560#67—416no—
561#67—416no—
562C2×Dic3—28no—
563C2×Dic3—28no—
564C2×Dic3—28no—
565C2×Dic3—22no—
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—416no—
584C2×Dic3—44no—
585C2×Dic3—44no—
586C2×Dic3—44no—
587C2×Dic3—44no—
588C2×Dic3C22×D414yes—
589C2×Dic3C22×D414yes—
590C2×Dic3C22×D414yes—
591C4×D3—416no—
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—22no—
612C24—34no—
613C24—32no—
614C24—62no—
615C24—62no—
616C24—62no—
617C24—62no—
618C24—62no—
619C24—62no—
620C24D3×D414yes—
621C24C23×D312yes—
622C24C23×D312yes—
623C24C23×D312yes—
624C24C23×D311yescharacteristic
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—316no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—416no—
636C2×D4—416no—
637C2×D4—416no—
638C2×D4—68no—
639C2×D4—68no—
640C2×D4—68no—
641C2×D4—124no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—1216no—
645C2×D4—124no—
646C2×D4—124no—
647C2×D4—1216no—
648C2×D4—1216no—
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—34no—
660C22×C4—34no—
661C22×C4—34no—
662C22×C4—32no—
663C22×C4—32no—
664C22×C4—32no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—68no—
670C22×C4—68no—
671C22×C4—62no—
672C22×C4—62no—
673C22×C4—62no—
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—68no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—68no—
691C22×C4—124no—
692C22×C4—1216no—
693C22×C4—124no—
694C22×C4—1216no—
695C22×C4D3×D414yes—
696C22×C4#23714yes—
697C22×C4C23×D312yes—
698C22×C4C23×D312yes—
699C22×C4C23×D312yes—
700C22×C4C23×D312yes—
701C4⋊C4—316no—
702C4⋊C4—68no—
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—44no—
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—68no—
722C22⋊C4—124no—
723C42—124no—
724C22×C3—24no—
725C22×C3—24no—
726C22×C3—24no—
727C22×C3—42no—
728C22×C3—416no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
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—88no—
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—24no—
763C2×D3—24no—
764C2×D3—24no—
765C2×D3—42no—
766C2×D3—416no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
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—28no—
788C23—28no—
789C23—28no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—34no—
805C23—44no—
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—44no—
822C23—44no—
823C23—62no—
824C23—62no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—68no—
830C23—68no—
831C23—68no—
832C23—124no—
833C23—124no—
834C23—124no—
835C23—124no—
836C23C2×D3×D414yes—
837C23C2×D3×D412yes—
838C23C2×D3×D412yes—
839C23C2×#23712yes—
840C23#100412yes—
841C23#100412yes—
842C23#100412yes—
843C23#101012yes—
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—44no—
867C2×C4—44no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—68no—
875C2×C4—68no—
876C2×C4—68no—
877C2×C4—62no—
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—1216no—
890C2×C4—1216no—
891C2×C4—124no—
892C2×C4—124no—
893C2×C4—124no—
894C2×C4—124no—
895C2×C4C2×D3×D414yes—
896C2×C4C2×#23714yes—
897C2×C3—44no—
898C2×C3—82no—
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—44no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—416no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—64no—
932C22—64no—
933C22—64no—
934C22—88no—
935C22—88no—
936C22—122no—
937C22—1216no—
938C22—122no—
939C22—122no—
940C22—122no—
941C22#558914yes—
942C22#559014yes—
943C22#559314yes—
944C22#560814yes—
945C22#561114yes—
946C22#562114yes—
947C22#571814yes—
948C22C22×D3×D411yescharacteristic
949C22C22×D3×D411yescharacteristic
950C22C22×#23711yescharacteristic
951C22C2×#100411yescharacteristic
952C22C2×#100411yescharacteristic
953C22C2×#100411yescharacteristic
954C22C2×#101011yescharacteristic
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—82no—
969C2—82no—
970C2—124no—
971C2#7671618yesdirect product factor
972C2C2×#559311yescharacteristic
973C2C2×#558911yescharacteristic
974C2C2×#559011yescharacteristic
975C2C2×#561111yescharacteristic
976C2C2×#560811yescharacteristic
977C2C2×#562111yescharacteristic
978C2C2×#571811yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#392C2
socleC24×C3C24
hypercenterC2×#392D3
hypocenterC3C2×#2682
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#938C2semidirect
2. C22×#935C2semidirect
3. C22×#939C2semidirect
4. C22×#883C2semidirect
5. C2×C3×#392C2semidirect
6. C2×#5223C2semidirect
7. C2×#5222C2semidirect
8. C2×#5221C2semidirect
9. C2×#4959C2semidirect
10. C2×#4948C2semidirect
11. C2×#4948C2semidirect
12. C2×#4957C2semidirect
13. C2×#4950C2semidirect
14. #76716C2direct (N × H)
15. C2×#4668C2semidirect
16. C2×#4647C2semidirect
38. C2×#939C22semidirect
40. C2×#938C22semidirect
42. C2×#935C22semidirect
56. C2×#883C22semidirect
57. C3×#392C22semidirect
59. #5223C22semidirect
60. #5222C22semidirect
61. #5221C22semidirect
65. #4959C22semidirect
66. #4957C22semidirect
67. #4950C22semidirect
68. #4948C22semidirect
69. #4948C22semidirect
70. #4668C22semidirect
71. #4647C22semidirect
82. C2×#392D3semidirect
116. C22×#67D4semidirect
176. C2×Dic3⋊C4D4semidirect
233. #392C2×D3semidirect
315. C2×#67C2×D4semidirect
373. Dic3⋊C4C2×D4semidirect
900. C2×C3#2682semidirect
966. C3C2×#2682semidirect
971. C2#76716direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9382
C22×#9352
C22×#9392
C22×#8832
C2×C3×#3922
C2×#52232
C2×#52222
C2×#52212
C2×#49592
C2×#49482
C2×#49572
C2×#49502
#767162
C2×#46682
C2×#46472
C2×#26823