Finite Group Databasebeta

← C2×#77010 #11430014

Subgroups — C2×#77010 #11430014

Order 768.

2894 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#935C211yesmaximal, characteristic
2C22×#878C211yesmaximal, characteristic, complemented
3C2×C3×#394C211yesmaximal, characteristic
4C2×#5220C211yesmaximal, characteristic
5C2×#4983C211yesmaximal, characteristic, complemented
6C2×#4982C211yesmaximal, characteristic, complemented
7C2×#4952C211yesmaximal, characteristic, complemented
8C2×#4947C211yesmaximal, characteristic, complemented
9C2×#4944C211yesmaximal, characteristic, complemented
10C2×#4951C211yesmaximal, characteristic, complemented
11C2×#4946C211yesmaximal, characteristic, complemented
12C2×#4943C211yesmaximal, characteristic, complemented
13C2×#4942C211yesmaximal, characteristic, complemented
14#77010C2116yesmaximal, direct product factor
15C2×#4658C211yesmaximal, characteristic, complemented
16C2×#4646C211yesmaximal, characteristic, complemented
17C2×#2687—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C2×#935—28no—
34C2×#935C2218yes—
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C2×#878—28no—
44C2×#878C2218yescomplemented
45C3×#394C2218yes—
46C2×C3×#95C2211yescharacteristic
47#5220C2218yes—
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59#4983C2218yescomplemented
60#4982C2218yescomplemented
61#4952C2218yescomplemented
62#4951C2218yescomplemented
63#4947C2218yescomplemented
64#4946C2218yescomplemented
65#4944C2218yescomplemented
66#4943C2218yescomplemented
67#4942C2218yescomplemented
68#4658C2218yescomplemented
69#4646C2218yescomplemented
70C22×#123—31no—
71C22×C22⋊Q8—31no—
72#2687—316no—
73C2×#400—31no—
74C2×#398—31no—
75C2×#398—31no—
76C2×#397—31no—
77C2×#394D311yescharacteristic
78C2×#393—31no—
79C2×#391—31no—
80C2×#388—31no—
81C2×#388—31no—
82C2×#386—31no—
83C2×#385—31no—
84C2×#381—31no—
85C2×#380—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C22×C3×D4—24no—
89C22×C3×D4—24no—
90C22×C3×D4—42no—
91C22×C3×D4C2314yes—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×Dic3—24no—
98C23×Dic3—24no—
99C23×Dic3—24no—
100C23×Dic3—24no—
101C23×Dic3—42no—
102C23×Dic3—42no—
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2314yes—
109C23×Dic3C2314yes—
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C22×Dic6—24no—
114C22×Dic6—24no—
115C22×Dic6—42no—
116C22×Dic6C2314yes—
117C2×C3×C4⋊C4—42no—
118C2×C3×C4⋊C4C2314yes—
119C2×C3×C22⋊C4—24no—
120C2×C3×C22⋊C4—24no—
121C2×C3×C22⋊C4—42no—
122C2×C3×C22⋊C4—42no—
123C2×C3×C22⋊C4C2314yes—
124C2×C3×C22⋊C4C2314yes—
125C2×C3×C22⋊C4C2314yes—
126C2×C3×C22⋊C4C2314yes—
127C2×#217—24no—
128C2×#217—24no—
129C2×#217—24no—
130C2×#217—42no—
131C2×#217—42no—
132C2×#217D418yes—
133C2×#217C2314yes—
134C2×#217C2314yes—
135C2×#217C2314yes—
136C2×#217C2314yes—
137C2×#217C2314yes—
138C2×#217C2314yes—
139#935—232no—
140C2×C4⋊Dic3—24no—
141C2×C4⋊Dic3C2314yes—
142C2×Dic3⋊C4—24no—
143C2×Dic3⋊C4—24no—
144C2×Dic3⋊C4—24no—
145C2×Dic3⋊C4—24no—
146C2×Dic3⋊C4—42no—
147C2×Dic3⋊C4—42no—
148C2×Dic3⋊C4C2314yes—
149C2×Dic3⋊C4C2314yes—
150C2×Dic3⋊C4C2314yes—
151C2×Dic3⋊C4C2314yes—
152C2×Dic3⋊C4C2314yes—
153C2×Dic3⋊C4C2314yes—
154C2×C4×Dic3—42no—
155C2×C4×Dic3C2314yes—
156#878—232no—
157C3×#95C2314yes—
158C3⋊#95C2314yes—
159C3⋊#95C2314yes—
160C3⋊#95C2314yes—
161C3⋊#95C2314yes—
162C3⋊#95C2314yes—
163C3⋊#95C2314yes—
164C3⋊#95C2314yes—
165C3⋊#95C2314yes—
166C3⋊#95C2314yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C23×Q8—31no—
170C23×D4C2×D311yescharacteristic
171C24×C4—31no—
172C24×C4—31no—
173C2×#123—38no—
174C2×#123—68no—
175C2×C22⋊Q8—38no—
176C2×C22⋊Q8—68no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4C2×D311yescharacteristic
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4C2×D311yescharacteristic
192C22×C22⋊C4C2×D311yescharacteristic
193C22×C22⋊C4C2×D311yescharacteristic
194C22×C22⋊C4C2×D311yescharacteristic
195C22×C42—31no—
196#400—38no—
197#398—38no—
198#398—38no—
199#397—38no—
200#394C2×D318yes—
201#393—38no—
202#391—38no—
203#388—38no—
204#388—38no—
205#386—38no—
206#385—38no—
207#381—38no—
208#380—38no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95C2×D311yescharacteristic
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3C2×D414yes—
234C24×C3#4114yes—
235C24×C3C2412yes—
236C24×C3C2412yes—
237C24×C3C2411yescharacteristic
238C2×C3×D4—28no—
239C2×C3×D4—28no—
240C2×C3×D4—44no—
241C2×C3×D4—416no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4C2412yes—
258C22×C3×C4C2412yes—
259C22×C3×C4C2412yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2412yes—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—28no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—28no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—28no—
286C22×Dic3—28no—
287C22×Dic3—44no—
288C22×Dic3—44no—
289C22×Dic3—416no—
290C22×Dic3—416no—
291C22×Dic3C2×D414yes—
292C22×Dic3C2×D414yes—
293C22×Dic3#4114yes—
294C22×Dic3C2412yes—
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298C22×Dic3C2412yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2412yes—
302C2×Dic6—28no—
303C2×Dic6—28no—
304C2×Dic6—44no—
305C2×Dic6—416no—
306C3×C4⋊C4—44no—
307C3×C22⋊C4—28no—
308C3×C22⋊C4—28no—
309C3×C22⋊C4—44no—
310C3×C22⋊C4—44no—
311#217—28no—
312#217—28no—
313#217—28no—
314#217—44no—
315#217—44no—
316#217C2×D4116yes—
317C4⋊Dic3—28no—
318Dic3⋊C4—28no—
319Dic3⋊C4—28no—
320Dic3⋊C4—28no—
321Dic3⋊C4—28no—
322Dic3⋊C4—44no—
323Dic3⋊C4—44no—
324C4×Dic3—44no—
325C25C22×D311yescharacteristic
326C25C22×D311yescharacteristic
327C22×Q8—34no—
328C22×Q8—64no—
329C22×Q8—64no—
330C22×Q8—122no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—42no—
334C22×D4C22×D314yes—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—31no—
338C23×C4—31no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—34no—
344C23×C4—34no—
345C23×C4—64no—
346C23×C4—64no—
347C23×C4—64no—
348C23×C4—64no—
349C23×C4—122no—
350C23×C4—122no—
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356#123—632no—
357C22⋊Q8—632no—
358C2×C4⋊C4—34no—
359C2×C4⋊C4—34no—
360C2×C4⋊C4—34no—
361C2×C4⋊C4—34no—
362C2×C4⋊C4—34no—
363C2×C4⋊C4—34no—
364C2×C4⋊C4—34no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—64no—
367C2×C4⋊C4—64no—
368C2×C4⋊C4—64no—
369C2×C4⋊C4—64no—
370C2×C4⋊C4—64no—
371C2×C4⋊C4—122no—
372C2×C4⋊C4—122no—
373C2×C4⋊C4C22×D314yes—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—38no—
377C2×C22⋊C4—34no—
378C2×C22⋊C4—34no—
379C2×C22⋊C4—34no—
380C2×C22⋊C4—34no—
381C2×C22⋊C4—34no—
382C2×C22⋊C4—34no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—64no—
386C2×C22⋊C4—64no—
387C2×C22⋊C4—64no—
388C2×C22⋊C4—122no—
389C2×C22⋊C4—122no—
390C2×C22⋊C4C22×D314yes—
391C2×C22⋊C4C22×D314yes—
392C2×C22⋊C4C22×D314yes—
393C2×C22⋊C4C22×D314yes—
394C2×C42—34no—
395C2×C42—122no—
396#95—34no—
397#95—34no—
398#95—34no—
399#95—34no—
400#95—34no—
401#95—34no—
402#95—34no—
403#95—34no—
404#95—34no—
405#95—34no—
406#95—34no—
407#95C22×D314yes—
408C23×C3—28no—
409C23×C3—28no—
410C23×C3—28no—
411C23×C3—28no—
412C23×C3—28no—
413C23×C3—28no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—44no—
427C23×C3—44no—
428C23×C3—44no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3C22×D414yes—
435C23×C3C22×D412yes—
436C23×C3C2×#4114yes—
437C23×C3C2×#4112yes—
438C23×C3C2×#4112yes—
439C23×C3H(5,𝔽2)12yes—
440C23×C3H(5,𝔽2)12yes—
441C23×C32−1+412yes—
442C23×C32−1+412yes—
443C23×C3C2511yescharacteristic
444C3×D4—416no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—44no—
461C2×C3×C4—44no—
462C2×C3×C4—44no—
463C2×C3×C4—44no—
464C2×C3×C4—44no—
465C2×Dic3—28no—
466C2×Dic3—28no—
467C2×Dic3—28no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—416no—
490C2×Dic3—416no—
491C2×Dic3—44no—
492C2×Dic3—44no—
493C2×Dic3—44no—
494C2×Dic3—44no—
495C2×Dic3—44no—
496C2×Dic3C22×D414yes—
497C2×Dic3C22×D414yes—
498C2×Dic3C2×#4114yes—
499Dic6—416no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24D3×D414yes—
513C24#23714yes—
514C24C23×D312yes—
515C24C23×D312yes—
516C24C23×D311yescharacteristic
517C2×Q8—68no—
518C2×Q8—68no—
519C2×Q8—124no—
520C2×Q8—1216no—
521C2×D4—28no—
522C2×D4—28no—
523C2×D4—44no—
524C2×D4—416no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—34no—
541C22×C4—34no—
542C22×C4—34no—
543C22×C4—32no—
544C22×C4—32no—
545C22×C4—32no—
546C22×C4—32no—
547C22×C4—32no—
548C22×C4—32no—
549C22×C4—32no—
550C22×C4—32no—
551C22×C4—68no—
552C22×C4—68no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—68no—
563C22×C4—68no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—124no—
577C22×C4—124no—
578C22×C4—1216no—
579C22×C4—1216no—
580C22×C4C23×D312yes—
581C22×C4C23×D312yes—
582C22×C4C23×D312yes—
583C22×C4C23×D312yes—
584C22×C4C23×D312yes—
585C4⋊C4—44no—
586C4⋊C4—68no—
587C4⋊C4—68no—
588C4⋊C4—68no—
589C4⋊C4—68no—
590C4⋊C4—68no—
591C4⋊C4—124no—
592C4⋊C4—124no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—316no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—68no—
599C22⋊C4—68no—
600C22⋊C4—68no—
601C22⋊C4—124no—
602C22⋊C4—124no—
603C42—124no—
604C22×C3—24no—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—416no—
615C22×C3—416no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3#53614yes—
621C22×C3#53914yes—
622C22×C3#54214yes—
623C22×C3#54614yes—
624C22×C3#54614yes—
625C22×C3#55214yes—
626C22×C3#56214yes—
627C22×C3C23×D411yescharacteristic
628C22×C3C22×#4111yescharacteristic
629C22×C3C22×#4111yescharacteristic
630C22×C3C2×H(5,𝔽2)11yescharacteristic
631C22×C3C2×H(5,𝔽2)11yescharacteristic
632C22×C3C2×2−1+411yescharacteristic
633C22×C3C2×2−1+411yescharacteristic
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—42no—
639Dic3—24no—
640Dic3—24no—
641Dic3—24no—
642Dic3—42no—
643Dic3—42no—
644Dic3—42no—
645Dic3—42no—
646Dic3—42no—
647C23—28no—
648C23—28no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23C2×D3×D414yes—
674C23C2×D3×D412yes—
675C23C2×#23714yes—
676C23C2×#23712yes—
677C23#100412yes—
678C23#100412yes—
679C23D3×#4112yes—
680C23#101012yes—
681C23#101012yes—
682C23C24×D311yescharacteristic
683Q8—1216no—
684D4—416no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—34no—
701C2×C4—34no—
702C2×C4—34no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—68no—
715C2×C4—68no—
716C2×C4—68no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—1216no—
733C2×C4—1216no—
734C2×C4—124no—
735C2×C4—124no—
736C2×C4—124no—
737C2×C4—124no—
738C2×C4—124no—
739C2×C3—44no—
740C2×C3—44no—
741C2×C3#268718yescomplemented
742C2×C3C2×#53611yescharacteristic
743C2×C3C2×#53911yescharacteristic
744C2×C3C2×#54211yescharacteristic
745C2×C3C2×#54611yescharacteristic
746C2×C3C2×#54611yescharacteristic
747C2×C3C2×#55211yescharacteristic
748C2×C3C2×#56211yescharacteristic
749C22—24no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—416no—
762C22—416no—
763C22—42no—
764C22—42no—
765C22#559114yes—
766C22#560214yes—
767C22#561014yes—
768C22#562114yes—
769C22#564814yes—
770C22#565014yes—
771C22#566914yes—
772C22C22×D3×D411yescharacteristic
773C22C22×#23711yescharacteristic
774C22C2×#100411yescharacteristic
775C22C2×#100411yescharacteristic
776C22C2×D3×#4111yescharacteristic
777C22C2×#101011yescharacteristic
778C22C2×#101011yescharacteristic
779C4—42no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—64no—
785C4—64no—
786C4—64no—
787C4—122no—
788C4—122no—
789C4—122no—
790C4—122no—
791C4—122no—
792C3C2×#268711yescharacteristic, complemented, Sylow
793C2—44no—
794C2—44no—
795C2#7701018yesdirect product factor
796C2C2×#559111yescharacteristic
797C2C2×#560211yescharacteristic
798C2C2×#561011yescharacteristic
799C2C2×#562111yescharacteristic
800C2C2×#564811yescharacteristic
801C2C2×#565011yescharacteristic
802C2C2×#566911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#394C2
socleC24×C3C24
prime radicalC23×C3×D4C22
hypercenterC2×#394D3
hypocenterC3C2×#2687
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#878C2semidirect
5. C2×#4983C2semidirect
6. C2×#4982C2semidirect
7. C2×#4952C2semidirect
8. C2×#4947C2semidirect
9. C2×#4944C2semidirect
10. C2×#4951C2semidirect
11. C2×#4946C2semidirect
12. C2×#4943C2semidirect
13. C2×#4942C2semidirect
14. #77010C2direct (N × H)
15. C2×#4658C2semidirect
16. C2×#4646C2semidirect
44. C2×#878C22semidirect
59. #4983C22semidirect
60. #4982C22semidirect
61. #4952C22semidirect
62. #4951C22semidirect
63. #4947C22semidirect
64. #4946C22semidirect
65. #4944C22semidirect
66. #4943C22semidirect
67. #4942C22semidirect
68. #4658C22semidirect
69. #4646C22semidirect
741. C2×C3#2687semidirect
792. C3C2×#2687semidirect
795. C2#77010direct (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×#8782
C2×C3×#3942
C2×#52202
C2×#49832
C2×#49822
C2×#49522
C2×#49472
C2×#49442
C2×#49512
C2×#49462
C2×#49432
C2×#49422
#770102
C2×#46582
C2×#46462
C2×#26873