Finite Group Databasebeta

← C2×#74775 #10965813

Subgroups — C2×#74775 #10965813

Order 768.

3502 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#926C211yesmaximal, characteristic, complemented
2C22×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C2×#5223C211yesmaximal, characteristic
5C2×#5220C211yesmaximal, characteristic, complemented
6C2×#5213C211yesmaximal, characteristic, complemented
7C2×#4956C211yesmaximal, characteristic, complemented
8C2×#4949C211yesmaximal, characteristic, complemented
9C2×#4961C211yesmaximal, characteristic, complemented
10C2×#4944C211yesmaximal, characteristic, complemented
11C2×#4950C211yesmaximal, characteristic, complemented
12#74775C2116yesmaximal, direct product factor
13C2×#4668C211yesmaximal, characteristic, complemented
14C2×#4660C211yesmaximal, characteristic, complemented
15C2×#4670C211yesmaximal, characteristic, complemented
16C2×#4651C211yesmaximal, characteristic, complemented
17C2×#2598—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C24×Dic3C2211yescharacteristic
23C23×C4×D3C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C2×#926—28no—
37C2×#926C2218yescomplemented
38C22×C4⋊Dic3C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×C4⋊Dic3C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×C4×Dic3C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C2×#67⋊C4—28no—
46C2×#67⋊C4C2218yescomplemented
47C3×#386C2218yescomplemented
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50#5223C2218yes—
51#5220C2218yescomplemented
52#5213C2218yescomplemented
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61#4961C2218yescomplemented
62#4956C2218yescomplemented
63#4950C2218yescomplemented
64#4949C2218yescomplemented
65#4944C2218yescomplemented
66#4670C2218yescomplemented
67#4668C2218yescomplemented
68#4660C2218yescomplemented
69#4651C2218yescomplemented
70C22×C4×D4—31no—
71C22×#117—31no—
72#2598—316no—
73C2×#400—31no—
74C2×#399—31no—
75C2×#394—31no—
76C2×#392—31no—
77C2×#388—31no—
78C2×#388—31no—
79C2×#386—31no—
80C2×#386—31no—
81C2×#386—31no—
82C2×#386D311yescharacteristic, complemented
83C2×#385—31no—
84C2×#385—31no—
85C2×#383—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C22×C3×D4—24no—
90C22×C3×D4—24no—
91C22×C3×D4—42no—
92C22×C3×D4C2314yes—
93C23×C3×C4—24no—
94C23×C3×C4—24no—
95C23×C3×C4—24no—
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2314yes—
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C22×#67—24no—
103C22×#67—24no—
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—42no—
108C22×#67C2314yes—
109C22×#67C2314yes—
110C23×Dic3—24no—
111C23×Dic3—42no—
112C23×Dic3—42no—
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2314yes—
121C22×C4×D3—24no—
122C22×C4×D3—42no—
123C22×C4×D3—42no—
124C22×C4×D3C2314yes—
125C2×C3×C22⋊C4—24no—
126C2×C3×C22⋊C4—24no—
127C2×C3×C22⋊C4—42no—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C22⋊C4C2314yes—
130C2×C3×C22⋊C4C2314yes—
131C2×#217—24no—
132C2×#217—24no—
133C2×#217—24no—
134C2×#217—42no—
135C2×#217—42no—
136C2×#217C2314yes—
137C2×#217C2314yes—
138C2×#217C2314yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4—24no—
143C2×(C2×D3)⋊C4—24no—
144C2×(C2×D3)⋊C4—42no—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149#926—232no—
150C2×C4⋊Dic3—24no—
151C2×C4⋊Dic3—24no—
152C2×C4⋊Dic3—42no—
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2314yes—
155C2×C4⋊Dic3C2314yes—
156C2×Dic3⋊C4—24no—
157C2×Dic3⋊C4—42no—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2314yes—
160C2×C4×Dic3—24no—
161C2×C4×Dic3D418yescomplemented
162C2×C4×Dic3C2314yes—
163C2×C4×Dic3C2314yes—
164#67⋊C4—232no—
165C3×#95C2314yes—
166C3×#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C23×D4—31no—
176C23×D4—31no—
177C23×D4C2×D311yescharacteristic
178C24×C4—31no—
179C24×C4—31no—
180C24×C4C2×D311yescharacteristic
181C2×C4×D4—38no—
182C2×C4×D4—68no—
183C2×#117—38no—
184C2×#117—68no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4C2×D311yescharacteristic
200C22×C22⋊C4C2×D311yescharacteristic
201C22×C22⋊C4C2×D311yescharacteristic
202C22×C42—31no—
203C22×C42—31no—
204#400—38no—
205#399—38no—
206#394—38no—
207#392—38no—
208#388—38no—
209#388—38no—
210#386—38no—
211#386—38no—
212#386—38no—
213#386C2×D318yescomplemented
214#385—38no—
215#385—38no—
216#383—38no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95C2×D311yescharacteristic
226C2×#95C2×D311yescharacteristic
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3#4114yes—
240C24×C3#4114yes—
241C24×C3C2412yes—
242C24×C3C2412yes—
243C24×C3C2411yescharacteristic
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3#4114yes—
251C23×D3C2412yes—
252C2×C3×D4—28no—
253C2×C3×D4—28no—
254C2×C3×D4—44no—
255C2×C3×D4—416no—
256C22×C3×C4—232no—
257C22×C3×C4—22no—
258C22×C3×C4—28no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—28no—
263C22×C3×C4—28no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4C2×D414yes—
274C22×C3×C4#4114yes—
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C2×#67—232no—
281C2×#67—28no—
282C2×#67—28no—
283C2×#67—28no—
284C2×#67—28no—
285C2×#67—28no—
286C2×#67—44no—
287C2×#67—416no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—22no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3—28no—
308C22×Dic3—44no—
309C22×Dic3—44no—
310C22×Dic3—416no—
311C22×Dic3C2×D414yes—
312C22×Dic3C2×D414yes—
313C22×Dic3C2412yes—
314C22×Dic3C2412yes—
315C22×Dic3C2412yes—
316C22×Dic3C2412yes—
317C22×Dic3C2412yes—
318C22×Dic3C2412yes—
319C22×Dic3C2412yes—
320C2×C4×D3—28no—
321C2×C4×D3—44no—
322C2×C4×D3—44no—
323C2×C4×D3—416no—
324C3×C22⋊C4—28no—
325C3×C22⋊C4—28no—
326C3×C22⋊C4—44no—
327#217—28no—
328#217—28no—
329#217—28no—
330#217—44no—
331#217—44no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—28no—
335(C2×D3)⋊C4—44no—
336C4⋊Dic3—28no—
337C4⋊Dic3—28no—
338C4⋊Dic3—44no—
339Dic3⋊C4—28no—
340Dic3⋊C4—44no—
341C4×Dic3—28no—
342C4×Dic3C2×D4116yescomplemented
343C25—31no—
344C25C22×D311yescharacteristic
345C25C22×D311yescharacteristic
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—34no—
349C22×D4—34no—
350C22×D4—42no—
351C22×D4—64no—
352C22×D4—64no—
353C22×D4—64no—
354C22×D4—64no—
355C22×D4—64no—
356C22×D4—122no—
357C22×D4C22×D314yes—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—34no—
369C23×C4—34no—
370C23×C4—64no—
371C23×C4—64no—
372C23×C4—122no—
373C23×C4—122no—
374C23×C4—122no—
375C23×C4—122no—
376C23×C4C22×D314yes—
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C4×D4—632no—
383#117—632no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—34no—
389C2×C4⋊C4—64no—
390C2×C4⋊C4—64no—
391C2×C4⋊C4—64no—
392C2×C4⋊C4—122no—
393C2×C4⋊C4—122no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—64no—
407C2×C22⋊C4—64no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—64no—
411C2×C22⋊C4—64no—
412C2×C22⋊C4—122no—
413C2×C22⋊C4—122no—
414C2×C22⋊C4—122no—
415C2×C22⋊C4C22×D314yes—
416C2×C22⋊C4C22×D314yes—
417C2×C22⋊C4C22×D314yes—
418C2×C42—38no—
419C2×C42—34no—
420C2×C42—34no—
421C2×C42—64no—
422#95—34no—
423#95—34no—
424#95—34no—
425#95—34no—
426#95—34no—
427#95—34no—
428#95—34no—
429#95—34no—
430#95C22×D314yes—
431#95C22×D314yes—
432C23×C3—28no—
433C23×C3—28no—
434C23×C3—28no—
435C23×C3—28no—
436C23×C3—28no—
437C23×C3—28no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—44no—
451C23×C3—44no—
452C23×C3—44no—
453C23×C3—44no—
454C23×C3—44no—
455C23×C3—44no—
456C23×C3—44no—
457C23×C3—44no—
458C23×C3C22×D412yes—
459C23×C3C2×#4114yes—
460C23×C3C2×#4112yes—
461C23×C3C2×#4114yes—
462C23×C3C2×#4112yes—
463C23×C3C2×#4112yes—
464C23×C3C2×#4112yes—
465C23×C3H(5,𝔽2)12yes—
466C23×C3H(5,𝔽2)12yes—
467C23×C3C2511yescharacteristic
468C22×D3—28no—
469C22×D3—28no—
470C22×D3—28no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—44no—
478C22×D3—44no—
479C22×D3—44no—
480C22×D3—44no—
481C22×D3C2×#4114yes—
482C3×D4—416no—
483C2×C3×C4—232no—
484C2×C3×C4—28no—
485C2×C3×C4—28no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—44no—
500C2×C3×C4—44no—
501C2×C3×C4—44no—
502C2×C3×C4C22×D414yes—
503C2×C3×C4C2×#4114yes—
504#67—232no—
505#67—416no—
506C2×Dic3—28no—
507C2×Dic3—28no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—416no—
528C2×Dic3—44no—
529C2×Dic3—44no—
530C2×Dic3—44no—
531C2×Dic3—44no—
532C2×Dic3—44no—
533C2×Dic3C22×D414yes—
534C2×Dic3C22×D414yes—
535C4×D3—416no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—34no—
549C24—32no—
550C24—62no—
551C24—62no—
552C24—62no—
553C24—62no—
554C24—62no—
555C24—62no—
556C24#23514yes—
557C24#23714yes—
558C24C23×D312yes—
559C24C23×D312yes—
560C24C23×D311yescharacteristic
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—44no—
564C2×D4—416no—
565C2×D4—68no—
566C2×D4—68no—
567C2×D4—632no—
568C2×D4—68no—
569C2×D4—68no—
570C2×D4—68no—
571C2×D4—124no—
572C2×D4—1216no—
573C22×C4—232no—
574C22×C4—22no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—34no—
591C22×C4—34no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—32no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—68no—
600C22×C4—68no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—124no—
621C22×C4—124no—
622C22×C4—1216no—
623C22×C4—124no—
624C22×C4—124no—
625C22×C4—1216no—
626C22×C4D3×D414yes—
627C22×C4#23714yes—
628C22×C4C23×D312yes—
629C22×C4C23×D312yes—
630C22×C4C23×D312yes—
631C22×C4C23×D312yes—
632C22×C4C23×D312yes—
633C4⋊C4—68no—
634C4⋊C4—68no—
635C4⋊C4—68no—
636C4⋊C4—124no—
637C4⋊C4—124no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—44no—
641C22⋊C4—68no—
642C22⋊C4—68no—
643C22⋊C4—68no—
644C22⋊C4—68no—
645C22⋊C4—68no—
646C22⋊C4—68no—
647C22⋊C4—124no—
648C22⋊C4—124no—
649C22⋊C4—124no—
650C42—316no—
651C42—68no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—24no—
656C22×C3—24no—
657C22×C3—24no—
658C22×C3—416no—
659C22×C3—416no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3#52514yes—
669C22×C3#52514yes—
670C22×C3#53514yes—
671C22×C3#55114yes—
672C22×C3#55114yes—
673C22×C3#55314yes—
674C22×C3#55314yes—
675C22×C3C23×D411yescharacteristic
676C22×C3C22×#4111yescharacteristic
677C22×C3C22×#4111yescharacteristic
678C22×C3C22×#4111yescharacteristic
679C22×C3C22×#4111yescharacteristic
680C22×C3C2×H(5,𝔽2)11yescharacteristic
681C22×C3C2×H(5,𝔽2)11yescharacteristic
682C2×D3—24no—
683C2×D3—24no—
684C2×D3—24no—
685C2×D3—416no—
686C2×D3—42no—
687C2×D3—42no—
688C2×D3—42no—
689C2×D3—42no—
690C3×C4—24no—
691C3×C4—24no—
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—42no—
695Dic3—24no—
696Dic3—24no—
697Dic3—42no—
698Dic3—42no—
699Dic3—42no—
700Dic3—42no—
701Dic3—42no—
702C23—28no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—28no—
720C23—34no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—68no—
730C23—62no—
731C23—62no—
732C23—62no—
733C23—62no—
734C23—62no—
735C23—62no—
736C23—68no—
737C23—68no—
738C23—124no—
739C23—124no—
740C23—124no—
741C23—124no—
742C23C2×#23514yes—
743C23C2×#23512yes—
744C23C2×D3×D412yes—
745C23C2×#23714yes—
746C23C2×#23712yes—
747C23C2×#23712yes—
748C23#100412yes—
749C23D3×#4112yes—
750C23#100912yes—
751C23C24×D311yescharacteristic
752D4—416no—
753D4—632no—
754D4—1216no—
755C2×C4—232no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—34no—
772C2×C4—34no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—68no—
781C2×C4—68no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—1216no—
798C2×C4—1216no—
799C2×C4—124no—
800C2×C4—124no—
801C2×C4—124no—
802C2×C4—124no—
803C2×C4—124no—
804C2×C4C2×D3×D414yes—
805C2×C4C2×#23714yes—
806C2×C3—44no—
807C2×C3—44no—
808C2×C3#259818yescomplemented
809C2×C3C2×#52511yescharacteristic
810C2×C3C2×#52511yescharacteristic
811C2×C3C2×#53511yescharacteristic
812C2×C3C2×#55111yescharacteristic
813C2×C3C2×#55111yescharacteristic
814C2×C3C2×#55311yescharacteristic
815C2×C3C2×#55311yescharacteristic
816D3—44no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—42no—
824C22—416no—
825C22—416no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—64no—
834C22—64no—
835C22—64no—
836C22—1216no—
837C22—122no—
838C22—122no—
839C22—122no—
840C22—122no—
841C22#549514yes—
842C22#554714yes—
843C22#556514yes—
844C22#558614yes—
845C22#560714yes—
846C22#561414yes—
847C22#565814yes—
848C22C22×#23511yescharacteristic
849C22C22×D3×D411yescharacteristic
850C22C22×#23711yescharacteristic
851C22C22×#23711yescharacteristic
852C22C2×#100411yescharacteristic
853C22C2×D3×#4111yescharacteristic
854C22C2×#100911yescharacteristic
855C4—24no—
856C4—24no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—64no—
861C4—64no—
862C4—122no—
863C4—122no—
864C4—122no—
865C4—122no—
866C4—122no—
867C3C2×#259811yescharacteristic, complemented, Sylow
868C2—44no—
869C2—44no—
870C2—124no—
871C2#7477518yesdirect product factor
872C2C2×#549511yescharacteristic
873C2C2×#556511yescharacteristic
874C2C2×#554711yescharacteristic
875C2C2×#558611yescharacteristic
876C2C2×#560711yescharacteristic
877C2C2×#561411yescharacteristic
878C2C2×#565811yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#386C2
socleC24×C3C24
prime radicalC2×#5223C2
hypercenterC2×#386D3
hypocenterC3C2×#2598
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#926C2semidirect
2. C22×#67⋊C4C2semidirect
3. C2×C3×#386C2semidirect
5. C2×#5220C2semidirect
6. C2×#5213C2semidirect
7. C2×#4956C2semidirect
8. C2×#4949C2semidirect
9. C2×#4961C2semidirect
10. C2×#4944C2semidirect
11. C2×#4950C2semidirect
12. #74775C2direct (N × H)
13. C2×#4668C2semidirect
14. C2×#4660C2semidirect
15. C2×#4670C2semidirect
16. C2×#4651C2semidirect
37. C2×#926C22semidirect
46. C2×#67⋊C4C22semidirect
47. C3×#386C22semidirect
51. #5220C22semidirect
52. #5213C22semidirect
61. #4961C22semidirect
62. #4956C22semidirect
63. #4950C22semidirect
64. #4949C22semidirect
65. #4944C22semidirect
66. #4670C22semidirect
67. #4668C22semidirect
68. #4660C22semidirect
69. #4651C22semidirect
82. C2×#386D3semidirect
161. C2×C4×Dic3D4semidirect
213. #386C2×D3semidirect
342. C4×Dic3C2×D4semidirect
808. C2×C3#2598semidirect
867. C3C2×#2598semidirect
871. C2#74775direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9262
C22×#67⋊C42
C2×C3×#3862
C2×#52232
C2×#52202
C2×#52132
C2×#49562
C2×#49492
C2×#49612
C2×#49442
C2×#49502
#747752
C2×#46682
C2×#46602
C2×#46702
C2×#46512
C2×#25983