Finite Group Databasebeta

← C2×#76710 #11429777

Subgroups — C2×#76710 #11429777

Order 768.

4042 conjugacy classes of subgroups.

The subgroup lattice has 984 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×#939C211yesmaximal, characteristic, complemented
5C2×C3×#392C211yesmaximal, characteristic, complemented
6C2×#5222C211yesmaximal, characteristic, complemented
7C2×#5220C211yesmaximal, characteristic, complemented
8C2×#4959C211yesmaximal, characteristic, complemented
9C2×#4956C211yesmaximal, characteristic, complemented
10C2×#4949C211yesmaximal, characteristic, complemented
11C2×#4961C211yesmaximal, characteristic, complemented
12C2×#4950C211yesmaximal, characteristic, complemented
13C2×#4946C211yesmaximal, characteristic, complemented
14#76710C2116yesmaximal, direct product factor
15C2×#4667C211yesmaximal, characteristic, complemented
16C2×#4657C211yesmaximal, characteristic, complemented
17C2×#2671—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C24×Dic3C2211yescharacteristic
25C24×Dic3C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C2×#939—28no—
38C2×#939—28no—
39C2×#939C2218yescomplemented
40C2×#939C2218yescomplemented
41C2×#938—28no—
42C2×#938C2218yescomplemented
43C2×#935—28no—
44C2×#935C2218yescomplemented
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C2211yescharacteristic
47C22×(C2×D3)⋊C4C2211yescharacteristic
48C22×C4⋊Dic3C2211yescharacteristic
49C22×C4⋊Dic3C2211yescharacteristic
50C22×Dic3⋊C4C2211yescharacteristic
51C22×Dic3⋊C4C2211yescharacteristic
52C22×Dic3⋊C4C2211yescharacteristic
53C22×Dic3⋊C4C2211yescharacteristic
54C22×Dic3⋊C4C2211yescharacteristic
55C3×#392C2218yescomplemented
56C2×C3×#95C2211yescharacteristic
57#5222C2218yescomplemented
58#5220C2218yescomplemented
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63C2×C3⋊#95C2211yescharacteristic
64#4961C2218yescomplemented
65#4959C2218yescomplemented
66#4956C2218yescomplemented
67#4950C2218yescomplemented
68#4949C2218yescomplemented
69#4946C2218yescomplemented
70#4667C2218yescomplemented
71#4657C2218yescomplemented
72C22×#123—31no—
73C22×#121—31no—
74C22×#121—31no—
75C22×#121—31no—
76#2671—316no—
77C2×#399—31no—
78C2×#398—31no—
79C2×#394—31no—
80C2×#394—31no—
81C2×#394—31no—
82C2×#392D311yescharacteristic, complemented
83C2×#386—31no—
84C2×#386—31no—
85C2×#385—31no—
86C2×#385—31no—
87C2×#380—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—24no—
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—24no—
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—24no—
123C23×Dic3—42no—
124C23×Dic3—42no—
125C23×Dic3—42no—
126C23×Dic3C2311yescharacteristic
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2311yescharacteristic
129C23×Dic3C2311yescharacteristic
130C23×Dic3C2314yes—
131C23×Dic3C2311yescharacteristic
132C23×Dic3C2311yescharacteristic
133C23×Dic3C2311yescharacteristic
134C23×Dic3C2314yes—
135C22×C4×D3—24no—
136C22×C4×D3—24no—
137C22×C4×D3—42no—
138C22×C4×D3C2314yes—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4—42no—
141C2×C3×C22⋊C4—42no—
142C2×C3×C22⋊C4C2314yes—
143C2×C3×C22⋊C4C2314yes—
144C2×C3×C22⋊C4C2314yes—
145C2×#217—24no—
146C2×#217—24no—
147C2×#217—24no—
148C2×#217—24no—
149C2×#217—24no—
150C2×#217—42no—
151C2×#217D418yescomplemented
152C2×#217C2314yes—
153C2×#217C2314yes—
154C2×#217C2314yes—
155C2×#217C2314yes—
156C2×#217C2314yes—
157C2×#217C2314yes—
158C2×#217C2314yes—
159#939—232no—
160#939—232no—
161#938—232no—
162#935—232no—
163C2×(C2×D3)⋊C4—24no—
164C2×(C2×D3)⋊C4—24no—
165C2×(C2×D3)⋊C4—42no—
166C2×(C2×D3)⋊C4C2314yes—
167C2×(C2×D3)⋊C4C2314yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×C4⋊Dic3—24no—
170C2×C4⋊Dic3—42no—
171C2×C4⋊Dic3C2314yes—
172C2×C4⋊Dic3C2314yes—
173C2×Dic3⋊C4—24no—
174C2×Dic3⋊C4—24no—
175C2×Dic3⋊C4—24no—
176C2×Dic3⋊C4—24no—
177C2×Dic3⋊C4—42no—
178C2×Dic3⋊C4C2314yes—
179C2×Dic3⋊C4C2314yes—
180C2×Dic3⋊C4C2314yes—
181C2×Dic3⋊C4C2314yes—
182C2×Dic3⋊C4C2314yes—
183C3×#95C2314yes—
184C3⋊#95C2314yes—
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—
197C24×C4—31no—
198C2×#123—38no—
199C2×#123—68no—
200C2×#121—38no—
201C2×#121—38no—
202C2×#121—38no—
203C2×#121—68no—
204C2×#121—68no—
205C2×#121—68no—
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⋊C4C2×D311yescharacteristic
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C22⋊C4C2×D311yescharacteristic
226#399—38no—
227#398—38no—
228#394—38no—
229#394—38no—
230#394—38no—
231#392C2×D318yescomplemented
232#386—38no—
233#386—38no—
234#385—38no—
235#385—38no—
236#380—38no—
237C2×#95—31no—
238C2×#95—31no—
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×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×D3C2×D414yes—
275C23×D3C2412yes—
276C2×C3×D4—28no—
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—28no—
280C2×C3×D4—28no—
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×C4—22no—
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—28no—
308C2×#67—416no—
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—22no—
328C22×Dic3—28no—
329C22×Dic3—22no—
330C22×Dic3—22no—
331C22×Dic3—22no—
332C22×Dic3—22no—
333C22×Dic3—22no—
334C22×Dic3—22no—
335C22×Dic3—28no—
336C22×Dic3—28no—
337C22×Dic3—44no—
338C22×Dic3—44no—
339C22×Dic3—44no—
340C22×Dic3—416no—
341C22×Dic3—416no—
342C22×Dic3C2×D414yes—
343C22×Dic3C2×D414yes—
344C22×Dic3C2×D414yes—
345C22×Dic3C2412yes—
346C22×Dic3C2412yes—
347C22×Dic3C2412yes—
348C22×Dic3C2412yes—
349C22×Dic3C2412yes—
350C22×Dic3C2412yes—
351C22×Dic3C2412yes—
352C2×C4×D3—28no—
353C2×C4×D3—28no—
354C2×C4×D3—44no—
355C2×C4×D3—416no—
356C3×C22⋊C4—28no—
357C3×C22⋊C4—44no—
358C3×C22⋊C4—44no—
359#217—28no—
360#217—28no—
361#217—28no—
362#217—28no—
363#217—28no—
364#217—44no—
365#217C2×D4116yescomplemented
366(C2×D3)⋊C4—28no—
367(C2×D3)⋊C4—28no—
368(C2×D3)⋊C4—44no—
369C4⋊Dic3—28no—
370C4⋊Dic3—44no—
371Dic3⋊C4—28no—
372Dic3⋊C4—28no—
373Dic3⋊C4—28no—
374Dic3⋊C4—28no—
375Dic3⋊C4—44no—
376C25—31no—
377C25C22×D311yescharacteristic
378C25C22×D311yescharacteristic
379C25C22×D311yescharacteristic
380C22×D4—24no—
381C22×D4—24no—
382C22×D4—24no—
383C22×D4—24no—
384C22×D4—24no—
385C22×D4—38no—
386C22×D4—34no—
387C22×D4—34no—
388C22×D4—34no—
389C22×D4—42no—
390C22×D4—42no—
391C22×D4—42no—
392C22×D4—42no—
393C22×D4—64no—
394C22×D4—64no—
395C22×D4—64no—
396C22×D4—64no—
397C22×D4—122no—
398C22×D4—122no—
399C22×D4—122no—
400C22×D4—122no—
401C22×D4C22×D314yes—
402C22×D4C22×D314yes—
403C22×D4C22×D314yes—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—34no—
412C23×C4—34no—
413C23×C4—34no—
414C23×C4—64no—
415C23×C4—64no—
416C23×C4—64no—
417C23×C4—64no—
418C23×C4—64no—
419C23×C4—122no—
420C23×C4—122no—
421C23×C4—122no—
422C23×C4—122no—
423C23×C4C22×D311yescharacteristic
424C23×C4C22×D311yescharacteristic
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427#123—632no—
428#121—632no—
429#121—632no—
430#121—632no—
431C2×C4⋊C4—34no—
432C2×C4⋊C4—34no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—34no—
436C2×C4⋊C4—34no—
437C2×C4⋊C4—34no—
438C2×C4⋊C4—64no—
439C2×C4⋊C4—64no—
440C2×C4⋊C4—64no—
441C2×C4⋊C4—64no—
442C2×C4⋊C4—64no—
443C2×C4⋊C4—122no—
444C2×C4⋊C4—122no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—38no—
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—34no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
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×C22⋊C4C22×D314yes—
471#95—34no—
472#95—34no—
473#95—34no—
474#95—34no—
475#95—34no—
476#95C22×D314yes—
477C23×C3—28no—
478C23×C3—28no—
479C23×C3—28no—
480C23×C3—28no—
481C23×C3—28no—
482C23×C3—28no—
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—22no—
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×D414yes—
519C23×C3C22×D412yes—
520C23×C3C22×D412yes—
521C23×C3C2×#4112yes—
522C23×C3H(5,𝔽2)12yes—
523C23×C3H(5,𝔽2)12yes—
524C23×C3H(5,𝔽2)12yes—
525C23×C32−1+412yes—
526C23×C3C2511yescharacteristic
527C22×D3—28no—
528C22×D3—28no—
529C22×D3—28no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—44no—
537C22×D3—44no—
538C22×D3—44no—
539C22×D3—44no—
540C22×D3C22×D414yes—
541C3×D4—416no—
542C3×D4—416no—
543C3×D4—416no—
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—22no—
556C2×C3×C4—44no—
557C2×C3×C4—44no—
558C2×C3×C4—44no—
559C2×C3×C4C2×#4114yes—
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—416no—
586C2×Dic3—44no—
587C2×Dic3—44no—
588C2×Dic3—44no—
589C2×Dic3—44no—
590C2×Dic3C22×D414yes—
591C2×Dic3C22×D414yes—
592C2×Dic3C22×D414yes—
593C4×D3—416no—
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—22no—
613C24—34no—
614C24—32no—
615C24—62no—
616C24—62no—
617C24—62no—
618C24—62no—
619C24—62no—
620C24—62no—
621C24D3×D414yes—
622C24D3×D414yes—
623C24C23×D312yes—
624C24C23×D312yes—
625C24C23×D312yes—
626C24C23×D311yescharacteristic
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—316no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—416no—
638C2×D4—416no—
639C2×D4—416no—
640C2×D4—68no—
641C2×D4—68no—
642C2×D4—68no—
643C2×D4—68no—
644C2×D4—124no—
645C2×D4—124no—
646C2×D4—124no—
647C2×D4—1216no—
648C2×D4—124no—
649C2×D4—1216no—
650C2×D4—1216no—
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—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—34no—
663C22×C4—34no—
664C22×C4—34no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—32no—
672C22×C4—68no—
673C22×C4—68no—
674C22×C4—68no—
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—68no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—68no—
695C22×C4—124no—
696C22×C4—1216no—
697C22×C4—124no—
698C22×C4—124no—
699C22×C4—124no—
700C22×C4—1216no—
701C22×C4—1216no—
702C22×C4#23714yes—
703C22×C4C23×D312yes—
704C22×C4C23×D312yes—
705C22×C4C23×D312yes—
706C22×C4C23×D312yes—
707C4⋊C4—68no—
708C4⋊C4—68no—
709C4⋊C4—68no—
710C4⋊C4—68no—
711C4⋊C4—68no—
712C4⋊C4—124no—
713C4⋊C4—124no—
714C22⋊C4—28no—
715C22⋊C4—316no—
716C22⋊C4—44no—
717C22⋊C4—44no—
718C22⋊C4—68no—
719C22⋊C4—68no—
720C22⋊C4—68no—
721C22⋊C4—68no—
722C22⋊C4—68no—
723C22⋊C4—68no—
724C22⋊C4—68no—
725C22⋊C4—124no—
726C22⋊C4—124no—
727C22×C3—24no—
728C22×C3—24no—
729C22×C3—24no—
730C22×C3—24no—
731C22×C3—24no—
732C22×C3—24no—
733C22×C3—416no—
734C22×C3—416no—
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—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—88no—
751C22×C3#53414yes—
752C22×C3#53714yes—
753C22×C3#54014yes—
754C22×C3D4214yes—
755C22×C3#54614yes—
756C22×C3#54714yes—
757C22×C3#56214yes—
758C22×C3C23×D411yescharacteristic
759C22×C3C23×D411yescharacteristic
760C22×C3C22×#4111yescharacteristic
761C22×C3C2×H(5,𝔽2)11yescharacteristic
762C22×C3C2×H(5,𝔽2)11yescharacteristic
763C22×C3C2×H(5,𝔽2)11yescharacteristic
764C22×C3C2×2−1+411yescharacteristic
765C2×D3—24no—
766C2×D3—24no—
767C2×D3—24no—
768C2×D3—416no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C3×C4—24no—
774C3×C4—42no—
775C3×C4—42no—
776C3×C4—42no—
777Dic3—24no—
778Dic3—24no—
779Dic3—24no—
780Dic3—42no—
781Dic3—42no—
782Dic3—42no—
783Dic3—42no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—28no—
797C23—28no—
798C23—28no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—34no—
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—44no—
824C23—44no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—62no—
830C23—62no—
831C23—68no—
832C23—68no—
833C23—68no—
834C23—124no—
835C23—124no—
836C23—124no—
837C23—124no—
838C23C2×D3×D414yes—
839C23C2×D3×D414yes—
840C23C2×D3×D412yes—
841C23C2×D3×D412yes—
842C23C2×#23712yes—
843C23#100412yes—
844C23#100412yes—
845C23#100412yes—
846C23#101012yes—
847C23C24×D311yescharacteristic
848D4—416no—
849D4—416no—
850D4—416no—
851D4—1216no—
852D4—1216no—
853D4—1216no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—28no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—34no—
867C2×C4—34no—
868C2×C4—34no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—62no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—68no—
879C2×C4—68no—
880C2×C4—68no—
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—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—1216no—
894C2×C4—1216no—
895C2×C4—1216no—
896C2×C4—124no—
897C2×C4—124no—
898C2×C4—124no—
899C2×C4—124no—
900C2×C4C2×#23714yes—
901C2×C3—44no—
902C2×C3—44no—
903C2×C3—82no—
904C2×C3#267118yescomplemented
905C2×C3C2×#53411yescharacteristic
906C2×C3C2×#53711yescharacteristic
907C2×C3C2×#54011yescharacteristic
908C2×C3C2×D4211yescharacteristic
909C2×C3C2×#54611yescharacteristic
910C2×C3C2×#54711yescharacteristic
911C2×C3C2×#56211yescharacteristic
912D3—44no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—416no—
923C22—416no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—64no—
937C22—64no—
938C22—64no—
939C22—88no—
940C22—122no—
941C22—122no—
942C22—1216no—
943C22—122no—
944C22—122no—
945C22#558914yes—
946C22#559014yes—
947C22#559114yes—
948C22#559714yes—
949C22#561114yes—
950C22#562114yes—
951C22#571914yes—
952C22C22×D3×D411yescharacteristic
953C22C22×D3×D411yescharacteristic
954C22C22×#23711yescharacteristic
955C22C2×#100411yescharacteristic
956C22C2×#100411yescharacteristic
957C22C2×#100411yescharacteristic
958C22C2×#101011yescharacteristic
959C4—24no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—64no—
964C4—64no—
965C4—64no—
966C4—122no—
967C4—122no—
968C4—122no—
969C4—122no—
970C3C2×#267111yescharacteristic, complemented, Sylow
971C2—44no—
972C2—44no—
973C2—82no—
974C2—124no—
975C2#7671018yesdirect product factor
976C2C2×#558911yescharacteristic
977C2C2×#559011yescharacteristic
978C2C2×#559111yescharacteristic
979C2C2×#559711yescharacteristic
980C2C2×#561111yescharacteristic
981C2C2×#562111yescharacteristic
982C2C2×#571911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#392C2
socleC24×C3C24
hypercenterC2×#392D3
hypocenterC3C2×#2671
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×#939C2semidirect
5. C2×C3×#392C2semidirect
6. C2×#5222C2semidirect
7. C2×#5220C2semidirect
8. C2×#4959C2semidirect
9. C2×#4956C2semidirect
10. C2×#4949C2semidirect
11. C2×#4961C2semidirect
12. C2×#4950C2semidirect
13. C2×#4946C2semidirect
14. #76710C2direct (N × H)
15. C2×#4667C2semidirect
16. C2×#4657C2semidirect
39. C2×#939C22semidirect
40. C2×#939C22semidirect
42. C2×#938C22semidirect
44. C2×#935C22semidirect
55. C3×#392C22semidirect
57. #5222C22semidirect
58. #5220C22semidirect
64. #4961C22semidirect
65. #4959C22semidirect
66. #4956C22semidirect
67. #4950C22semidirect
68. #4949C22semidirect
69. #4946C22semidirect
70. #4667C22semidirect
71. #4657C22semidirect
82. C2×#392D3semidirect
116. C22×#67D4semidirect
151. C2×#217D4semidirect
231. #392C2×D3semidirect
315. C2×#67C2×D4semidirect
365. #217C2×D4semidirect
904. C2×C3#2671semidirect
970. C3C2×#2671semidirect
975. C2#76710direct (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
C2×C3×#3922
C2×#52222
C2×#52202
C2×#49592
C2×#49562
C2×#49492
C2×#49612
C2×#49502
C2×#49462
#767102
C2×#46672
C2×#46572
C2×#26713