Finite Group Databasebeta

← C2×#82687 #11429988

Subgroups — C2×#82687 #11429988

Order 768.

3218 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×C3×#121C211yesmaximal, characteristic
2C22×#936C211yesmaximal, characteristic, complemented
3C2×#5222C211yesmaximal, characteristic, complemented
4C2×#5222C211yesmaximal, characteristic, complemented
5C2×#5222C211yesmaximal, characteristic, complemented
6C2×#5220C211yesmaximal, characteristic, complemented
7C2×#5220C211yesmaximal, characteristic, complemented
8C2×#5210C211yesmaximal, characteristic, complemented
9C2×#5211C211yesmaximal, characteristic, complemented
10#82687C2116yesmaximal, direct product factor
11C2×#4979C211yesmaximal, characteristic, complemented
12C2×#4978C211yesmaximal, characteristic, complemented
13C2×#4952C211yesmaximal, characteristic, complemented
14C2×#4947C211yesmaximal, characteristic, complemented
15C2×#4944C211yesmaximal, characteristic, complemented
16C2×#4942C211yesmaximal, characteristic, complemented
17C2×#2686—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C24×Dic3C2211yescharacteristic
23C23×Dic6C2211yescharacteristic
24C2×C3×#121—28no—
25C2×C3×#121C2218yes—
26C22×C3×C4⋊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
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C22×#217C2211yescharacteristic
40C2×#936—28no—
41C2×#936C2218yescomplemented
42C22×Dic3⋊C4C2211yescharacteristic
43C22×Dic3⋊C4C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×C4×Dic3C2211yescharacteristic
47#5222C2218yescomplemented
48#5222C2218yescomplemented
49#5222C2218yescomplemented
50#5220C2218yescomplemented
51#5220C2218yescomplemented
52#5211C2218yescomplemented
53#5210C2218yescomplemented
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2211yescharacteristic
63C2×C3⋊#95C2211yescharacteristic
64#4979C2218yescomplemented
65#4978C2218yescomplemented
66#4952C2218yescomplemented
67#4947C2218yescomplemented
68#4944C2218yescomplemented
69#4942C2218yescomplemented
70C22×#124—31no—
71C22×#121D311yescharacteristic
72#2686—316no—
73C2×#397—31no—
74C2×#395—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#394—31no—
78C2×#393—31no—
79C2×#388—31no—
80C2×#387—31no—
81C2×#386—31no—
82C2×#386—31no—
83C2×#385—31no—
84C2×#381—31no—
85C2×#380—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C22×C3×D4—24no—
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—42no—
93C22×C3×D4—42no—
94C22×C3×D4—42no—
95C22×C3×D4—42no—
96C22×C3×D4—42no—
97C22×C3×D4D418yes—
98C22×C3×D4C2314yes—
99C22×C3×D4C2314yes—
100C22×C3×D4C2314yes—
101C23×C3×C4—24no—
102C23×C3×C4—24no—
103C23×C3×C4—42no—
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2314yes—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×Dic3—24no—
110C23×Dic3—42no—
111C23×Dic3—42no—
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2314yes—
121C22×Dic6—24no—
122C22×Dic6—42no—
123C22×Dic6—42no—
124C22×Dic6C2314yes—
125C3×#121—232no—
126C2×C3×C4⋊C4—24no—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C22⋊C4—24no—
129C2×C3×C22⋊C4—24no—
130C2×C3×C22⋊C4C2314yes—
131C2×C3×C22⋊C4C2314yes—
132C2×#217—24no—
133C2×#217—24no—
134C2×#217—24no—
135C2×#217—24no—
136C2×#217—24no—
137C2×#217—24no—
138C2×#217—42no—
139C2×#217—42no—
140C2×#217—42no—
141C2×#217—42no—
142C2×#217—42no—
143C2×#217C2314yes—
144C2×#217C2314yes—
145C2×#217C2314yes—
146C2×#217C2314yes—
147C2×#217C2314yes—
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×#217C2314yes—
153C2×#217C2314yes—
154#936—232no—
155C2×Dic3⋊C4—24no—
156C2×Dic3⋊C4—42no—
157C2×Dic3⋊C4—42no—
158C2×Dic3⋊C4—42no—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×C4×Dic3—24no—
164C2×C4×Dic3C2314yes—
165C3⋊#95C2314yes—
166C3⋊#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C23×Q8—31no—
176C23×D4C2×D311yescharacteristic
177C23×D4C2×D311yescharacteristic
178C23×D4C2×D311yescharacteristic
179C24×C4—31no—
180C24×C4C2×D311yescharacteristic
181C2×#124—38no—
182C2×#124—68no—
183C2×#121—28no—
184C2×#121C2×D318yes—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4C2×D311yescharacteristic
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×C42—31no—
204#397—38no—
205#395—38no—
206#394—38no—
207#394—38no—
208#394—38no—
209#393—38no—
210#388—38no—
211#387—38no—
212#386—38no—
213#386—38no—
214#385—38no—
215#381—38no—
216#380—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×#95—31no—
226C2×#95—31no—
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×C3C2×D414yes—
247C24×C3C2×D414yes—
248C24×C3C2412yes—
249C24×C3C2412yes—
250C24×C3C2412yes—
251C24×C3C2411yescharacteristic
252C2×C3×D4—28no—
253C2×C3×D4—28no—
254C2×C3×D4—28no—
255C2×C3×D4—416no—
256C2×C3×D4—44no—
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×D4C2×D4116yes—
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—28no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—28no—
276C22×C3×C4—44no—
277C22×C3×C4—416no—
278C22×C3×C4C2×D414yes—
279C22×C3×C4#4114yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2412yes—
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—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×Dic3#4114yes—
312C22×Dic3C2412yes—
313C22×Dic3C2412yes—
314C22×Dic3C2412yes—
315C22×Dic3C2412yes—
316C22×Dic3C2412yes—
317C22×Dic3C2412yes—
318C22×Dic3C2412yes—
319C22×Dic3C2412yes—
320C2×Dic6—28no—
321C2×Dic6—44no—
322C2×Dic6—44no—
323C2×Dic6—416no—
324C3×C4⋊C4—28no—
325C3×C22⋊C4—28no—
326C3×C22⋊C4—28no—
327#217—28no—
328#217—28no—
329#217—28no—
330#217—28no—
331#217—28no—
332#217—28no—
333#217—44no—
334#217—44no—
335#217—44no—
336#217—44no—
337#217—44no—
338Dic3⋊C4—28no—
339Dic3⋊C4—44no—
340Dic3⋊C4—44no—
341Dic3⋊C4—44no—
342C4×Dic3—28no—
343C25C22×D311yescharacteristic
344C25C22×D311yescharacteristic
345C25C22×D311yescharacteristic
346C22×Q8—34no—
347C22×Q8—64no—
348C22×Q8—122no—
349C22×Q8—122no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4#6718yes—
359C22×D4C22×D314yes—
360C22×D4C22×D314yes—
361C22×D4C22×D314yes—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—31no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—34no—
373C23×C4—42no—
374C23×C4—64no—
375C23×C4—122no—
376C23×C4—122no—
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D314yes—
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382#124—632no—
383#121—232no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—34no—
389C2×C4⋊C4—64no—
390C2×C4⋊C4—122no—
391C2×C4⋊C4—122no—
392C2×C4⋊C4—122no—
393C2×C4⋊C4C22×D314yes—
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—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—64no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4—64no—
410C2×C22⋊C4—64no—
411C2×C22⋊C4—64no—
412C2×C22⋊C4—64no—
413C2×C22⋊C4—122no—
414C2×C22⋊C4—122no—
415C2×C22⋊C4—122no—
416C2×C22⋊C4—122no—
417C2×C22⋊C4—122no—
418C2×C22⋊C4C22×D314yes—
419C2×C22⋊C4C22×D314yes—
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#95—34no—
431#95—34no—
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—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
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×C3—44no—
472C23×C3C22×D414yes—
473C23×C3C22×D414yes—
474C23×C3C22×D412yes—
475C23×C3C2×#4112yes—
476C23×C3C2×#4112yes—
477C23×C3H(5,𝔽2)12yes—
478C23×C3H(5,𝔽2)12yes—
479C23×C3H(5,𝔽2)12yes—
480C23×C32−1+412yes—
481C23×C3C2511yescharacteristic
482C3×D4—416no—
483C3×D4—416no—
484C3×D4—416no—
485C2×C3×C4—28no—
486C2×C3×C4—28no—
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—416no—
498C2×C3×C4—44no—
499C2×C3×C4—44no—
500C2×C3×C4C22×D414yes—
501C2×C3×C4C2×#4114yes—
502C2×Dic3—28no—
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—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—416no—
527C2×Dic3—44no—
528C2×Dic3—44no—
529C2×Dic3—44no—
530C2×Dic3—44no—
531C2×Dic3—44no—
532C2×Dic3—44no—
533C2×Dic3—44no—
534C2×Dic3C2×#4114yes—
535Dic6—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—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24C2×#6714yes—
556C24C2×#6714yes—
557C24C23×D312yes—
558C24C23×D312yes—
559C24C23×D312yes—
560C24C23×D311yescharacteristic
561C2×Q8—68no—
562C2×Q8—124no—
563C2×Q8—124no—
564C2×Q8—1216no—
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—416no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—416no—
575C2×D4—416no—
576C2×D4C2×#67116yes—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—34no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—32no—
597C22×C4—32no—
598C22×C4—44no—
599C22×C4—416no—
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—62no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—124no—
625C22×C4—124no—
626C22×C4—1216no—
627C22×C4#23714yes—
628C22×C4C2×#6714yes—
629C22×C4C23×D312yes—
630C22×C4C23×D312yes—
631C22×C4C23×D312yes—
632C22×C4C23×D312yes—
633C4⋊C4—28no—
634C4⋊C4—68no—
635C4⋊C4—124no—
636C4⋊C4—124no—
637C4⋊C4—124no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—68no—
641C22⋊C4—68no—
642C22⋊C4—68no—
643C22⋊C4—68no—
644C22⋊C4—68no—
645C22⋊C4—68no—
646C22⋊C4—124no—
647C22⋊C4—124no—
648C22⋊C4—124no—
649C22⋊C4—124no—
650C22⋊C4—124no—
651C42—68no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—24no—
656C22×C3—24no—
657C22×C3—24no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—416no—
661C22×C3—416no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—88no—
676C22×C3#53414yes—
677C22×C3#53814yes—
678C22×C3#54214yes—
679C22×C3#54614yes—
680C22×C3#54714yes—
681C22×C3#55514yes—
682C22×C3#56214yes—
683C22×C3C23×D411yescharacteristic
684C22×C3C22×#4111yescharacteristic
685C22×C3C22×#4111yescharacteristic
686C22×C3C2×H(5,𝔽2)11yescharacteristic
687C22×C3C2×H(5,𝔽2)11yescharacteristic
688C22×C3C2×H(5,𝔽2)11yescharacteristic
689C22×C3C2×2−1+411yescharacteristic
690C3×C4—24no—
691C3×C4—24no—
692C3×C4—42no—
693C3×C4—42no—
694Dic3—24no—
695Dic3—42no—
696Dic3—42no—
697Dic3—42no—
698Dic3—42no—
699Dic3—42no—
700Dic3—42no—
701Dic3—42no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—28no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23C2×#23712yes—
743C23#100412yes—
744C23#100412yes—
745C23#100412yes—
746C23D3×#4112yes—
747C23#101012yes—
748C23C22×#6714yes—
749C23C22×#6714yes—
750C23C22×#6712yes—
751C23C24×D311yescharacteristic
752Q8—1216no—
753D4—416no—
754D4—416no—
755D4—416no—
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—34no—
769C2×C4—416no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—68no—
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—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—1216no—
797C2×C4—124no—
798C2×C4—124no—
799C2×C4—124no—
800C2×C4—124no—
801C2×C4—124no—
802C2×C4—124no—
803C2×C4—124no—
804C2×C4C2×#23714yes—
805C2×C4C22×#6714yes—
806C2×C3—44no—
807C2×C3—44no—
808C2×C3—82no—
809C2×C3#268618yescomplemented
810C2×C3C2×#53411yescharacteristic
811C2×C3C2×#53811yescharacteristic
812C2×C3C2×#54211yescharacteristic
813C2×C3C2×#54611yescharacteristic
814C2×C3C2×#54711yescharacteristic
815C2×C3C2×#55511yescharacteristic
816C2×C3C2×#56211yescharacteristic
817C22—24no—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—416no—
832C22—416no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—88no—
841C22#560314yes—
842C22#561314yes—
843C22#561614yes—
844C22#562114yes—
845C22#580414yes—
846C22#580614yes—
847C22#582414yes—
848C22C22×#23711yescharacteristic
849C22C2×#100411yescharacteristic
850C22C2×#100411yescharacteristic
851C22C2×#100411yescharacteristic
852C22C2×D3×#4111yescharacteristic
853C22C2×#101011yescharacteristic
854C22C23×#6711yescharacteristic
855C4—24no—
856C4—24no—
857C4—42no—
858C4—42no—
859C4—64no—
860C4—122no—
861C4—122no—
862C4—122no—
863C4—122no—
864C4—122no—
865C4—122no—
866C4—122no—
867C3C2×#268611yescharacteristic, complemented, Sylow
868C2—44no—
869C2—44no—
870C2—82no—
871C2#8268718yesdirect product factor
872C2C2×#560311yescharacteristic
873C2C2×#561611yescharacteristic
874C2C2×#561311yescharacteristic
875C2C2×#562111yescharacteristic
876C2C2×#580611yescharacteristic
877C2C2×#580411yescharacteristic
878C2C2×#582411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
Fitting, prime radicalC22×C3×#121C2
socleC24×C3C24
hypercenterC22×#121D3
hypocenterC3C2×#2686
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
2. C22×#936C2semidirect
3. C2×#5222C2semidirect
4. C2×#5222C2semidirect
5. C2×#5222C2semidirect
6. C2×#5220C2semidirect
7. C2×#5220C2semidirect
8. C2×#5210C2semidirect
9. C2×#5211C2semidirect
10. #82687C2direct (N × H)
11. C2×#4979C2semidirect
12. C2×#4978C2semidirect
13. C2×#4952C2semidirect
14. C2×#4947C2semidirect
15. C2×#4944C2semidirect
16. C2×#4942C2semidirect
41. C2×#936C22semidirect
47. #5222C22semidirect
48. #5222C22semidirect
49. #5222C22semidirect
50. #5220C22semidirect
51. #5220C22semidirect
52. #5211C22semidirect
53. #5210C22semidirect
64. #4979C22semidirect
65. #4978C22semidirect
66. #4952C22semidirect
67. #4947C22semidirect
68. #4944C22semidirect
69. #4942C22semidirect
809. C2×C3#2686semidirect
867. C3C2×#2686semidirect
871. C2#82687direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C22×#9362
C2×#52222
C2×#52202
C2×#52102
C2×#52112
#826872
C2×#49792
C2×#49782
C2×#49522
C2×#49472
C2×#49442
C2×#49422
C2×#26863