Finite Group Databasebeta

← C2×#76689 #10965261

Subgroups — C2×#76689 #10965261

Order 768.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#935C211yesmaximal, characteristic, complemented
2C22×#879C211yesmaximal, characteristic, complemented
3C2×C3×#392C211yesmaximal, characteristic
4C2×#5222C211yesmaximal, characteristic, complemented
5C2×#5221C211yesmaximal, characteristic, complemented
6C2×#5221C211yesmaximal, characteristic, complemented
7C2×#5221C211yesmaximal, characteristic, complemented
8C2×#5220C211yesmaximal, characteristic, complemented
9C2×#4948C211yesmaximal, characteristic, complemented
10C2×#4945C211yesmaximal, characteristic, complemented
11C2×#4944C211yesmaximal, characteristic, complemented
12C2×#4951C211yesmaximal, characteristic, complemented
13C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
14#76689C2116yesmaximal, direct product factor
15C2×#4661C211yesmaximal, characteristic, complemented
16C2×#4649C211yesmaximal, characteristic, complemented
17C2×#2554—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C24×Dic3C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C2×#935—28no—
37C2×#935C2218yescomplemented
38C22×C4⋊Dic3C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×C4⋊Dic3C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×C4×Dic3C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47C22×C4×Dic3C2211yescharacteristic
48C22×C4×Dic3C2211yescharacteristic
49C2×#879—28no—
50C2×#879C2218yescomplemented
51C3×#392C2218yes—
52C2×C3×#95C2211yescharacteristic
53#5222C2218yescomplemented
54#5221C2218yescomplemented
55#5221C2218yescomplemented
56#5221C2218yescomplemented
57#5220C2218yescomplemented
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63#4951C2218yescomplemented
64#4948C2218yescomplemented
65#4945C2218yescomplemented
66#4944C2218yescomplemented
67Dic3×C22⋊C4C2218yescomplemented
68#4661C2218yescomplemented
69#4649C2218yescomplemented
70C22×#126—31no—
71C22×#123—31no—
72#2554—316no—
73C2×#398—31no—
74C2×#396—31no—
75C2×#394—31no—
76C2×#392D311yescharacteristic
77C2×#390—31no—
78C2×#390—31no—
79C2×#390—31no—
80C2×#388—31no—
81C2×#388—31no—
82C2×#388—31no—
83C2×#386—31no—
84C2×C4×C4⋊C4—31no—
85C2×C4×C22⋊C4—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C22×C3×D4—24no—
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4—42no—
95C22×C3×D4—42no—
96C22×C3×D4—42no—
97C22×C3×D4—42no—
98C22×C3×D4C2314yes—
99C22×C3×D4C2314yes—
100C22×C3×D4C2314yes—
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×Dic3—24no—
106C23×Dic3—24no—
107C23×Dic3—42no—
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2314yes—
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C2×C3×C22⋊C4—24no—
118C2×C3×C22⋊C4—24no—
119C2×C3×C22⋊C4—24no—
120C2×C3×C22⋊C4C2314yes—
121C2×C3×C22⋊C4C2314yes—
122C2×C3×C22⋊C4C2314yes—
123C2×#217—24no—
124C2×#217—24no—
125C2×#217—24no—
126C2×#217—24no—
127C2×#217—24no—
128C2×#217—24no—
129C2×#217—24no—
130C2×#217—24no—
131C2×#217—42no—
132C2×#217—42no—
133C2×#217—42no—
134C2×#217C2314yes—
135C2×#217C2314yes—
136C2×#217C2314yes—
137C2×#217C2314yes—
138C2×#217C2314yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×#217C2314yes—
142C2×#217C2314yes—
143C2×#217C2314yes—
144C2×#217C2314yes—
145#935—232no—
146C2×C4⋊Dic3—24no—
147C2×C4⋊Dic3—42no—
148C2×C4⋊Dic3—42no—
149C2×C4⋊Dic3C2314yes—
150C2×C4⋊Dic3C2314yes—
151C2×C4⋊Dic3C2314yes—
152C2×Dic3⋊C4—24no—
153C2×Dic3⋊C4—24no—
154C2×Dic3⋊C4—24no—
155C2×Dic3⋊C4D418yescomplemented
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2314yes—
160C2×C4×Dic3—24no—
161C2×C4×Dic3—24no—
162C2×C4×Dic3—42no—
163C2×C4×Dic3—42no—
164C2×C4×Dic3C2314yes—
165C2×C4×Dic3C2314yes—
166C2×C4×Dic3C2314yes—
167C2×C4×Dic3C2314yes—
168#879—232no—
169C3×#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C23×D4C2×D311yescharacteristic
176C23×D4C2×D311yescharacteristic
177C23×D4C2×D311yescharacteristic
178C24×C4—31no—
179C2×#126—38no—
180C2×#126—68no—
181C2×#123—38no—
182C2×#123—68no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
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⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4C2×D311yescharacteristic
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C22⋊C4C2×D311yescharacteristic
204C22×C42—31no—
205C22×C42—31no—
206C22×C42—31no—
207C22×C42—31no—
208#398—38no—
209#396—38no—
210#394—38no—
211#392C2×D318yes—
212#390—38no—
213#390—38no—
214#390—38no—
215#388—38no—
216#388—38no—
217#388—38no—
218#386—38no—
219C4×C4⋊C4—38no—
220C4×C22⋊C4—38no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
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—22no—
240C24×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3#4114yes—
248C24×C3C2412yes—
249C24×C3C2412yes—
250C24×C3C2412yes—
251C24×C3C2411yescharacteristic
252C2×C3×D4—28no—
253C2×C3×D4—28no—
254C2×C3×D4—28no—
255C2×C3×D4—28no—
256C2×C3×D4—28no—
257C2×C3×D4—44no—
258C2×C3×D4—44no—
259C2×C3×D4—44no—
260C2×C3×D4—44no—
261C2×C3×D4—416no—
262C2×C3×D4—416no—
263C2×C3×D4—416no—
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×C4#4114yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—28no—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—28no—
303C22×Dic3—44no—
304C22×Dic3—416no—
305C22×Dic3C2×D414yes—
306C22×Dic3C2×D414yes—
307C22×Dic3#4114yes—
308C22×Dic3C2412yes—
309C22×Dic3C2412yes—
310C22×Dic3C2412yes—
311C22×Dic3C2412yes—
312C22×Dic3C2412yes—
313C22×Dic3C2412yes—
314C22×Dic3C2412yes—
315C22×Dic3C2412yes—
316C3×C22⋊C4—28no—
317C3×C22⋊C4—28no—
318C3×C22⋊C4—28no—
319#217—28no—
320#217—28no—
321#217—28no—
322#217—28no—
323#217—28no—
324#217—28no—
325#217—28no—
326#217—28no—
327#217—44no—
328#217—44no—
329#217—44no—
330C4⋊Dic3—28no—
331C4⋊Dic3—44no—
332C4⋊Dic3—44no—
333Dic3⋊C4—28no—
334Dic3⋊C4—28no—
335Dic3⋊C4—28no—
336Dic3⋊C4C2×D4116yescomplemented
337C4×Dic3—28no—
338C4×Dic3—28no—
339C4×Dic3—44no—
340C4×Dic3—44no—
341C25C22×D311yescharacteristic
342C25C22×D311yescharacteristic
343C25C22×D311yescharacteristic
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4C22×D314yes—
354C22×D4C22×D314yes—
355C22×D4C22×D314yes—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—34no—
365C23×C4—64no—
366C23×C4—64no—
367C23×C4—122no—
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C23×C4C22×D311yescharacteristic
372#126—632no—
373#123—632no—
374C2×C4⋊C4—38no—
375C2×C4⋊C4—34no—
376C2×C4⋊C4—34no—
377C2×C4⋊C4—34no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—34no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—64no—
383C2×C4⋊C4—64no—
384C2×C4⋊C4—64no—
385C2×C4⋊C4—64no—
386C2×C4⋊C4—122no—
387C2×C4⋊C4—122no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—34no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—34no—
395C2×C22⋊C4—34no—
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—64no—
403C2×C22⋊C4—64no—
404C2×C22⋊C4—64no—
405C2×C22⋊C4—64no—
406C2×C22⋊C4—64no—
407C2×C22⋊C4—64no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—122no—
411C2×C22⋊C4—122no—
412C2×C22⋊C4—122no—
413C2×C22⋊C4C22×D314yes—
414C2×C22⋊C4C22×D314yes—
415C2×C22⋊C4C22×D314yes—
416C2×C42—34no—
417C2×C42—34no—
418C2×C42—34no—
419C2×C42—34no—
420C2×C42—64no—
421C2×C42—64no—
422C2×C42—122no—
423C2×C42—122no—
424#95—34no—
425#95—34no—
426#95—34no—
427#95—34no—
428#95—34no—
429#95C22×D314yes—
430C23×C3—28no—
431C23×C3—28no—
432C23×C3—28no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
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—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—44no—
454C23×C3—44no—
455C23×C3—44no—
456C23×C3—44no—
457C23×C3—44no—
458C23×C3—44no—
459C23×C3—44no—
460C23×C3—44no—
461C23×C3—44no—
462C23×C3—44no—
463C23×C3—44no—
464C23×C3—44no—
465C23×C3—44no—
466C23×C3—44no—
467C23×C3—44no—
468C23×C3—44no—
469C23×C3—44no—
470C23×C3—44no—
471C23×C3C22×D412yes—
472C23×C3C2×#4114yes—
473C23×C3C2×#4112yes—
474C23×C3C2×#4112yes—
475C23×C3C2×#4112yes—
476C23×C3C2×#4112yes—
477C23×C3H(5,𝔽2)12yes—
478C23×C3H(5,𝔽2)12yes—
479C23×C3C2511yescharacteristic
480C3×D4—416no—
481C3×D4—416no—
482C3×D4—416no—
483C2×C3×C4—28no—
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—44no—
496C2×C3×C4C22×D414yes—
497C2×C3×C4C2×#4114yes—
498C2×C3×C4C2×#4114yes—
499C2×Dic3—28no—
500C2×Dic3—28no—
501C2×Dic3—28no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
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—416no—
524C2×Dic3—44no—
525C2×Dic3—44no—
526C2×Dic3—44no—
527C2×Dic3—44no—
528C2×Dic3—44no—
529C2×Dic3C22×D414yes—
530C2×Dic3C22×D414yes—
531C2×Dic3C2×#4114yes—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
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—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24#23714yes—
553C24C23×D312yes—
554C24C23×D312yes—
555C24C23×D312yes—
556C24C23×D311yescharacteristic
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—416no—
567C2×D4—416no—
568C2×D4—416no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—34no—
579C22×C4—34no—
580C22×C4—34no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—32no—
585C22×C4—32no—
586C22×C4—32no—
587C22×C4—32no—
588C22×C4—32no—
589C22×C4—68no—
590C22×C4—62no—
591C22×C4—62no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—62no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4—68no—
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—124no—
613C22×C4—1216no—
614C22×C4D3×D414yes—
615C22×C4#23714yes—
616C22×C4#23714yes—
617C22×C4C23×D312yes—
618C22×C4C23×D312yes—
619C22×C4C23×D312yes—
620C22×C4C23×D312yes—
621C4⋊C4—316no—
622C4⋊C4—68no—
623C4⋊C4—68no—
624C4⋊C4—68no—
625C4⋊C4—68no—
626C4⋊C4—124no—
627C4⋊C4—124no—
628C22⋊C4—28no—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—68no—
632C22⋊C4—68no—
633C22⋊C4—68no—
634C22⋊C4—68no—
635C22⋊C4—68no—
636C22⋊C4—68no—
637C22⋊C4—68no—
638C22⋊C4—68no—
639C22⋊C4—124no—
640C22⋊C4—124no—
641C22⋊C4—124no—
642C42—68no—
643C42—68no—
644C42—124no—
645C42—124no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—416no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
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—88no—
669C22×C3—88no—
670C22×C3#52914yes—
671C22×C3#53214yes—
672C22×C3#53814yes—
673C22×C3#54614yes—
674C22×C3#55014yes—
675C22×C3#55114yes—
676C22×C3#55314yes—
677C22×C3C23×D411yescharacteristic
678C22×C3C22×#4111yescharacteristic
679C22×C3C22×#4111yescharacteristic
680C22×C3C22×#4111yescharacteristic
681C22×C3C22×#4111yescharacteristic
682C22×C3C2×H(5,𝔽2)11yescharacteristic
683C22×C3C2×H(5,𝔽2)11yescharacteristic
684C3×C4—24no—
685C3×C4—24no—
686C3×C4—24no—
687C3×C4—42no—
688Dic3—24no—
689Dic3—24no—
690Dic3—24no—
691Dic3—42no—
692Dic3—42no—
693Dic3—42no—
694Dic3—42no—
695Dic3—42no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—28no—
703C23—28no—
704C23—28no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23C2×D3×D412yes—
738C23C2×#23714yes—
739C23C2×#23712yes—
740C23C2×#23712yes—
741C23C2×#23712yes—
742C23#100412yes—
743C23#100412yes—
744C23D3×#4112yes—
745C23C24×D311yescharacteristic
746D4—416no—
747D4—416no—
748D4—416no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—34no—
762C2×C4—34no—
763C2×C4—34no—
764C2×C4—44no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—68no—
772C2×C4—68no—
773C2×C4—68no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—1216no—
790C2×C4—124no—
791C2×C4—124no—
792C2×C4—124no—
793C2×C4—124no—
794C2×C4—124no—
795C2×C4C2×D3×D414yes—
796C2×C4C2×#23714yes—
797C2×C4C2×#23714yes—
798C2×C3—44no—
799C2×C3—82no—
800C2×C3—82no—
801C2×C3#255418yescomplemented
802C2×C3C2×#52911yescharacteristic
803C2×C3C2×#53211yescharacteristic
804C2×C3C2×#53811yescharacteristic
805C2×C3C2×#54611yescharacteristic
806C2×C3C2×#55011yescharacteristic
807C2×C3C2×#55111yescharacteristic
808C2×C3C2×#55311yescharacteristic
809C22—24no—
810C22—24no—
811C22—24no—
812C22—416no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—88no—
832C22—88no—
833C22#558714yes—
834C22#559114yes—
835C22#559314yes—
836C22#559914yes—
837C22#560014yes—
838C22#561414yes—
839C22#571614yes—
840C22C22×D3×D411yescharacteristic
841C22C22×#23711yescharacteristic
842C22C22×#23711yescharacteristic
843C22C22×#23711yescharacteristic
844C22C2×#100411yescharacteristic
845C22C2×#100411yescharacteristic
846C22C2×D3×#4111yescharacteristic
847C4—24no—
848C4—24no—
849C4—24no—
850C4—42no—
851C4—64no—
852C4—64no—
853C4—64no—
854C4—122no—
855C4—122no—
856C4—122no—
857C4—122no—
858C4—122no—
859C3C2×#255411yescharacteristic, complemented, Sylow
860C2—44no—
861C2—82no—
862C2—82no—
863C2#7668918yesdirect product factor
864C2C2×#559311yescharacteristic
865C2C2×#558711yescharacteristic
866C2C2×#559111yescharacteristic
867C2C2×#560011yescharacteristic
868C2C2×#559911yescharacteristic
869C2C2×#561411yescharacteristic
870C2C2×#571611yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
Fitting, prime radicalC2×C3×#392C2
socleC24×C3C24
hypercenterC2×#392D3
hypocenterC3C2×#2554
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#935C2semidirect
2. C22×#879C2semidirect
4. C2×#5222C2semidirect
5. C2×#5221C2semidirect
6. C2×#5221C2semidirect
7. C2×#5221C2semidirect
8. C2×#5220C2semidirect
9. C2×#4948C2semidirect
10. C2×#4945C2semidirect
11. C2×#4944C2semidirect
12. C2×#4951C2semidirect
13. C2×Dic3×C22⋊C4C2semidirect
14. #76689C2direct (N × H)
15. C2×#4661C2semidirect
16. C2×#4649C2semidirect
37. C2×#935C22semidirect
50. C2×#879C22semidirect
53. #5222C22semidirect
54. #5221C22semidirect
55. #5221C22semidirect
56. #5221C22semidirect
57. #5220C22semidirect
63. #4951C22semidirect
64. #4948C22semidirect
65. #4945C22semidirect
66. #4944C22semidirect
67. Dic3×C22⋊C4C22semidirect
68. #4661C22semidirect
69. #4649C22semidirect
155. C2×Dic3⋊C4D4semidirect
336. Dic3⋊C4C2×D4semidirect
801. C2×C3#2554semidirect
859. C3C2×#2554semidirect
863. C2#76689direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9352
C22×#8792
C2×C3×#3922
C2×#52222
C2×#52212
C2×#52202
C2×#49482
C2×#49452
C2×#49442
C2×#49512
C2×Dic3×C22⋊C42
#766892
C2×#46612
C2×#46492
C2×#25543