Finite Group Databasebeta

← C2×#77130 #11429768

Subgroups — C2×#77130 #11429768

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×#939C211yesmaximal, characteristic, complemented
2C22×#939C211yesmaximal, characteristic, complemented
3C22×#883C211yesmaximal, characteristic, complemented
4C22×#884C211yesmaximal, characteristic, complemented
5C2×C3×#394C211yesmaximal, characteristic, complemented
6C2×#4993C211yesmaximal, characteristic, complemented
7C2×#4989C211yesmaximal, characteristic, complemented
8C2×#4960C211yesmaximal, characteristic, complemented
9C2×#4961C211yesmaximal, characteristic, complemented
10C2×#4958C211yesmaximal, characteristic, complemented
11C2×#4958C211yesmaximal, characteristic, complemented
12C2×#4946C211yesmaximal, characteristic, complemented
13C2×#4942C211yesmaximal, characteristic, complemented
14#77130C2116yesmaximal, direct product factor
15C2×#4657C211yesmaximal, characteristic, complemented
16C2×#4672C211yesmaximal, characteristic, complemented
17C2×#2671—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C24×Dic3C2211yescharacteristic
24C24×Dic3C2211yescharacteristic
25C23×D12C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C2×#939—28no—
35C2×#939—28no—
36C2×#939C2218yescomplemented
37C2×#939C2218yescomplemented
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×C4⋊Dic3C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×Dic3⋊C4C2211yescharacteristic
49C22×Dic3⋊C4C2211yescharacteristic
50C22×Dic3⋊C4C2211yescharacteristic
51C2×#884—28no—
52C2×#884C2218yescomplemented
53C2×#883—28no—
54C2×#883C2218yescomplemented
55C3×#394C2218yescomplemented
56C2×C3×#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62#4993C2218yescomplemented
63#4989C2218yescomplemented
64#4961C2218yescomplemented
65#4960C2218yescomplemented
66#4958C2218yescomplemented
67#4958C2218yescomplemented
68#4946C2218yescomplemented
69#4942C2218yescomplemented
70#4672C2218yescomplemented
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×#394D311yescharacteristic, complemented
82C2×#392—31no—
83C2×#386—31no—
84C2×#386—31no—
85C2×#385—31no—
86C2×#385—31no—
87C2×#380—31no—
88C25×C3C2311yescharacteristic
89C25×C3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C24×D3C2311yescharacteristic
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4—42no—
95C22×C3×D4C2314yes—
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C22×#67—24no—
102C22×#67—24no—
103C22×#67—24no—
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—42no—
108C22×#67—42no—
109C22×#67—42no—
110C22×#67—42no—
111C22×#67—42no—
112C22×#67D418yescomplemented
113C22×#67C2314yes—
114C22×#67C2314yes—
115C22×#67C2314yes—
116C22×#67C2314yes—
117C23×Dic3—24no—
118C23×Dic3—24no—
119C23×Dic3—24no—
120C23×Dic3—42no—
121C23×Dic3—42no—
122C23×Dic3—42no—
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2314yes—
126C23×Dic3C2311yescharacteristic
127C23×Dic3C2311yescharacteristic
128C23×Dic3C2311yescharacteristic
129C23×Dic3C2311yescharacteristic
130C23×Dic3C2314yes—
131C22×D12—24no—
132C22×D12—42no—
133C22×D12—42no—
134C22×D12C2314yes—
135C22×C4×D3—24no—
136C22×C4×D3—24no—
137C22×C4×D3—42no—
138C22×C4×D3C2314yes—
139C2×C3×C4⋊C4—42no—
140C2×C3×C4⋊C4C2314yes—
141C2×C3×C22⋊C4—24no—
142C2×C3×C22⋊C4—24no—
143C2×C3×C22⋊C4—42no—
144C2×C3×C22⋊C4—42no—
145C2×C3×C22⋊C4C2314yes—
146C2×C3×C22⋊C4C2314yes—
147C2×C3×C22⋊C4C2314yes—
148C2×C3×C22⋊C4C2314yes—
149C2×#217—24no—
150C2×#217D418yescomplemented
151C2×#217C2314yes—
152C2×#217C2314yes—
153#939—232no—
154#939—232no—
155C2×(C2×D3)⋊C4—24no—
156C2×(C2×D3)⋊C4—24no—
157C2×(C2×D3)⋊C4—24no—
158C2×(C2×D3)⋊C4—24no—
159C2×(C2×D3)⋊C4—24no—
160C2×(C2×D3)⋊C4—42no—
161C2×(C2×D3)⋊C4—42no—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×(C2×D3)⋊C4C2314yes—
166C2×(C2×D3)⋊C4C2314yes—
167C2×(C2×D3)⋊C4C2314yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×C4⋊Dic3—24no—
170C2×C4⋊Dic3C2314yes—
171C2×Dic3⋊C4—24no—
172C2×Dic3⋊C4—24no—
173C2×Dic3⋊C4—24no—
174C2×Dic3⋊C4—24no—
175C2×Dic3⋊C4—42no—
176C2×Dic3⋊C4C2314yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179C2×Dic3⋊C4C2314yes—
180C2×Dic3⋊C4C2314yes—
181#884—232no—
182#883—232no—
183C3×#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—31no—
192C23×D4—31no—
193C23×D4—31no—
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⋊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⋊C4C2×D311yescharacteristic
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#394C2×D318yescomplemented
231#392—38no—
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×C3C2×D414yes—
256C24×C3C2×D414yes—
257C24×C3C2412yes—
258C24×C3C2412yes—
259C24×C3C2411yescharacteristic
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—22no—
263C23×D3—22no—
264C23×D3—22no—
265C23×D3—22no—
266C23×D3—22no—
267C23×D3—22no—
268C23×D3—22no—
269C23×D3—22no—
270C23×D3—22no—
271C23×D3—22no—
272C23×D3—22no—
273C23×D3C2×D414yes—
274C23×D3C2412yes—
275C23×D3C2412yes—
276C2×C3×D4—28no—
277C2×C3×D4—28no—
278C2×C3×D4—44no—
279C2×C3×D4—416no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
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×C4C2412yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2412yes—
298C22×C3×C4C2412yes—
299C22×C3×C4C2412yes—
300C2×#67—28no—
301C2×#67—28no—
302C2×#67—28no—
303C2×#67—28no—
304C2×#67—28no—
305C2×#67—28no—
306C2×#67—416no—
307C2×#67—44no—
308C2×#67—44no—
309C2×#67—44no—
310C2×#67—44no—
311C2×#67—44no—
312C2×#67—416no—
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—22no—
329C22×Dic3—22no—
330C22×Dic3—28no—
331C22×Dic3—28no—
332C22×Dic3—28no—
333C22×Dic3—44no—
334C22×Dic3—44no—
335C22×Dic3—44no—
336C22×Dic3—416no—
337C22×Dic3—416no—
338C22×Dic3C2×D414yes—
339C22×Dic3C2×D414yes—
340C22×Dic3C2×D414yes—
341C22×Dic3#4114yes—
342C22×Dic3C2412yes—
343C22×Dic3C2412yes—
344C22×Dic3C2412yes—
345C22×Dic3C2412yes—
346C22×Dic3C2412yes—
347C22×Dic3C2412yes—
348C2×D12—28no—
349C2×D12—44no—
350C2×D12—44no—
351C2×D12—416no—
352C2×C4×D3—28no—
353C2×C4×D3—28no—
354C2×C4×D3—44no—
355C2×C4×D3—416no—
356C3×C4⋊C4—44no—
357C3×C22⋊C4—28no—
358C3×C22⋊C4—28no—
359C3×C22⋊C4—44no—
360C3×C22⋊C4—44no—
361#217—28no—
362#217C2×D4116yescomplemented
363(C2×D3)⋊C4—28no—
364(C2×D3)⋊C4—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—28no—
367(C2×D3)⋊C4—28no—
368(C2×D3)⋊C4—44no—
369(C2×D3)⋊C4—44no—
370C4⋊Dic3—28no—
371Dic3⋊C4—28no—
372Dic3⋊C4—28no—
373Dic3⋊C4—28no—
374Dic3⋊C4—28no—
375Dic3⋊C4—44no—
376C25—31no—
377C25—31no—
378C25C22×D311yescharacteristic
379C25C22×D311yescharacteristic
380C22×D4—24no—
381C22×D4—24no—
382C22×D4—38no—
383C22×D4—34no—
384C22×D4—34no—
385C22×D4—34no—
386C22×D4—34no—
387C22×D4—34no—
388C22×D4—42no—
389C22×D4—64no—
390C22×D4—64no—
391C22×D4—64no—
392C22×D4—64no—
393C22×D4—64no—
394C22×D4—64no—
395C22×D4—64no—
396C22×D4—122no—
397C22×D4—122no—
398C22×D4—122no—
399C22×D4—122no—
400C22×D4—122no—
401C22×D4—122no—
402C22×D4—122no—
403C22×D4C22×D314yes—
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—34no—
413C23×C4—64no—
414C23×C4—64no—
415C23×C4—64no—
416C23×C4—64no—
417C23×C4—64no—
418C23×C4—122no—
419C23×C4—122no—
420C23×C4—122no—
421C23×C4—122no—
422C23×C4C22×D311yescharacteristic
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—42no—
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⋊C4C22×D314yes—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—38no—
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—122no—
466C2×C22⋊C4—122no—
467C2×C22⋊C4C22×D314yes—
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—44no—
496C23×C3—44no—
497C23×C3—44no—
498C23×C3—44no—
499C23×C3—44no—
500C23×C3—44no—
501C23×C3—44no—
502C23×C3—44no—
503C23×C3C22×D414yes—
504C23×C3C22×D414yes—
505C23×C3C22×D412yes—
506C23×C3C22×D412yes—
507C23×C3C2×#4112yes—
508C23×C3H(5,𝔽2)12yes—
509C23×C3H(5,𝔽2)12yes—
510C23×C3H(5,𝔽2)12yes—
511C23×C32−1+412yes—
512C23×C3C2511yescharacteristic
513C22×D3—28no—
514C22×D3—28no—
515C22×D3—28no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—44no—
530C22×D3—44no—
531C22×D3—44no—
532C22×D3—44no—
533C22×D3—44no—
534C22×D3—44no—
535C22×D3—44no—
536C22×D3—44no—
537C22×D3—44no—
538C22×D3—44no—
539C22×D3—44no—
540C22×D3C22×D414yes—
541C3×D4—416no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
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—22no—
557C2×C3×C4—44no—
558C2×C3×C4—44no—
559C2×C3×C4—44no—
560C2×C3×C4—44no—
561C2×C3×C4—44no—
562#67—416no—
563#67—416no—
564#67—416no—
565#67—416no—
566C2×Dic3—28no—
567C2×Dic3—28no—
568C2×Dic3—28no—
569C2×Dic3—28no—
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×Dic3C22×D414yes—
589C2×Dic3C22×D414yes—
590C2×Dic3C22×D414yes—
591C2×Dic3C2×#4114yes—
592D12—416no—
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—34no—
607C24—32no—
608C24—32no—
609C24—62no—
610C24—62no—
611C24—62no—
612C24—62no—
613C24—62no—
614C24—62no—
615C24—62no—
616C24—62no—
617C24—62no—
618C24—62no—
619C24—62no—
620C24—62no—
621C24—62no—
622C24D3×D414yes—
623C24D3×D414yes—
624C24C23×D312yes—
625C24C23×D312yes—
626C24C23×D311yescharacteristic
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—316no—
630C2×D4—44no—
631C2×D4—416no—
632C2×D4—68no—
633C2×D4—68no—
634C2×D4—68no—
635C2×D4—68no—
636C2×D4—68no—
637C2×D4—68no—
638C2×D4—68no—
639C2×D4—124no—
640C2×D4—124no—
641C2×D4—1216no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C2×D4—124no—
646C2×D4—1216no—
647C2×D4—124no—
648C2×D4—1216no—
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—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—34no—
667C22×C4—34no—
668C22×C4—34no—
669C22×C4—34no—
670C22×C4—32no—
671C22×C4—32no—
672C22×C4—32no—
673C22×C4—32no—
674C22×C4—32no—
675C22×C4—32no—
676C22×C4—68no—
677C22×C4—68no—
678C22×C4—68no—
679C22×C4—68no—
680C22×C4—68no—
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—62no—
693C22×C4—62no—
694C22×C4—62no—
695C22×C4—124no—
696C22×C4—1216no—
697C22×C4—124no—
698C22×C4—124no—
699C22×C4—124no—
700C22×C4—1216no—
701C22×C4—1216no—
702C22×C4C23×D312yes—
703C22×C4C23×D312yes—
704C22×C4C23×D312yes—
705C22×C4C23×D312yes—
706C22×C4C23×D312yes—
707C4⋊C4—44no—
708C4⋊C4—68no—
709C4⋊C4—68no—
710C4⋊C4—68no—
711C4⋊C4—68no—
712C4⋊C4—68no—
713C4⋊C4—124no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—316no—
717C22⋊C4—44no—
718C22⋊C4—44no—
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#53414yes—
744C22×C3#53714yes—
745C22×C3#54014yes—
746C22×C3D4214yes—
747C22×C3#54614yes—
748C22×C3#54714yes—
749C22×C3#56214yes—
750C22×C3C23×D411yescharacteristic
751C22×C3C23×D411yescharacteristic
752C22×C3C22×#4111yescharacteristic
753C22×C3C2×H(5,𝔽2)11yescharacteristic
754C22×C3C2×H(5,𝔽2)11yescharacteristic
755C22×C3C2×H(5,𝔽2)11yescharacteristic
756C22×C3C2×2−1+411yescharacteristic
757C2×D3—24no—
758C2×D3—24no—
759C2×D3—24no—
760C2×D3—416no—
761C2×D3—42no—
762C2×D3—42no—
763C2×D3—42no—
764C2×D3—42no—
765C2×D3—42no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—88no—
773C3×C4—42no—
774C3×C4—42no—
775C3×C4—42no—
776C3×C4—42no—
777C3×C4—42no—
778Dic3—24no—
779Dic3—24no—
780Dic3—24no—
781Dic3—24no—
782Dic3—42no—
783Dic3—42no—
784C23—28no—
785C23—28no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—28no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—34no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—68no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—68no—
819C23—68no—
820C23—62no—
821C23—62no—
822C23—62no—
823C23—62no—
824C23—62no—
825C23—62no—
826C23—62no—
827C23—124no—
828C23—124no—
829C23—124no—
830C23—124no—
831C23—124no—
832C23—124no—
833C23—124no—
834C23—124no—
835C23—124no—
836C23—124no—
837C23—124no—
838C23C2×D3×D414yes—
839C23C2×D3×D414yes—
840C23C2×D3×D412yes—
841C23C2×D3×D412yes—
842C23#100412yes—
843C23#100412yes—
844C23D3×#4112yes—
845C23#100912yes—
846C23#101012yes—
847C23C24×D311yescharacteristic
848D4—416no—
849D4—1216no—
850D4—1216no—
851D4—1216no—
852D4—1216no—
853D4—1216no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
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—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—34no—
870C2×C4—34no—
871C2×C4—34no—
872C2×C4—34no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—68no—
879C2×C4—68no—
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—68no—
889C2×C4—68no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—62no—
896C2×C4—1216no—
897C2×C4—1216no—
898C2×C4—1216no—
899C2×C4—124no—
900C2×C4—124no—
901C2×C3—44no—
902C2×C3—44no—
903C2×C3#267118yescomplemented
904C2×C3C2×#53411yescharacteristic
905C2×C3C2×#53711yescharacteristic
906C2×C3C2×#54011yescharacteristic
907C2×C3C2×D4211yescharacteristic
908C2×C3C2×#54611yescharacteristic
909C2×C3C2×#54711yescharacteristic
910C2×C3C2×#56211yescharacteristic
911D3—44no—
912D3—82no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—42no—
920C22—42no—
921C22—416no—
922C22—416no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—64no—
930C22—64no—
931C22—64no—
932C22—122no—
933C22—1216no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22—122no—
938C22—122no—
939C22—122no—
940C22—122no—
941C22—122no—
942C22—122no—
943C22—122no—
944C22—248no—
945C22#559014yes—
946C22#559714yes—
947C22#560514yes—
948C22#561514yes—
949C22#565414yes—
950C22#565514yes—
951C22#568414yes—
952C22C22×D3×D411yescharacteristic
953C22C22×D3×D411yescharacteristic
954C22C2×#100411yescharacteristic
955C22C2×#100411yescharacteristic
956C22C2×D3×#4111yescharacteristic
957C22C2×#100911yescharacteristic
958C22C2×#101011yescharacteristic
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—64no—
965C4—64no—
966C4—64no—
967C4—64no—
968C4—122no—
969C4—122no—
970C3C2×#267111yescharacteristic, complemented, Sylow
971C2—44no—
972C2—44no—
973C2—124no—
974C2—242no—
975C2#7713018yesdirect product factor
976C2C2×#559011yescharacteristic
977C2C2×#559711yescharacteristic
978C2C2×#561511yescharacteristic
979C2C2×#560511yescharacteristic
980C2C2×#565411yescharacteristic
981C2C2×#565511yescharacteristic
982C2C2×#568411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#394C2
socleC24×C3C24
hypercenterC2×#394D3
hypocenterC3C2×#2671
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#939C2semidirect
2. C22×#939C2semidirect
3. C22×#883C2semidirect
4. C22×#884C2semidirect
5. C2×C3×#394C2semidirect
6. C2×#4993C2semidirect
7. C2×#4989C2semidirect
8. C2×#4960C2semidirect
9. C2×#4961C2semidirect
10. C2×#4958C2semidirect
11. C2×#4958C2semidirect
12. C2×#4946C2semidirect
13. C2×#4942C2semidirect
14. #77130C2direct (N × H)
15. C2×#4657C2semidirect
16. C2×#4672C2semidirect
36. C2×#939C22semidirect
37. C2×#939C22semidirect
52. C2×#884C22semidirect
54. C2×#883C22semidirect
55. C3×#394C22semidirect
62. #4993C22semidirect
63. #4989C22semidirect
64. #4961C22semidirect
65. #4960C22semidirect
66. #4958C22semidirect
67. #4958C22semidirect
68. #4946C22semidirect
69. #4942C22semidirect
70. #4672C22semidirect
71. #4657C22semidirect
81. C2×#394D3semidirect
112. C22×#67D4semidirect
150. C2×#217D4semidirect
230. #394C2×D3semidirect
315. C2×#67C2×D4semidirect
362. #217C2×D4semidirect
903. C2×C3#2671semidirect
970. C3C2×#2671semidirect
975. C2#77130direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9392
C22×#8832
C22×#8842
C2×C3×#3942
C2×#49932
C2×#49892
C2×#49602
C2×#49612
C2×#49582
C2×#49462
C2×#49422
#771302
C2×#46572
C2×#46722
C2×#26713