Finite Group Databasebeta

← #10726579

Subgroups — #10726579

Order 768.

3654 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×#878C211yesmaximal, characteristic, complemented
3C2×#4955C211yesmaximal, characteristic
4C2×#4955C211yesmaximal, characteristic
5C2×#4673C212yesmaximal, complemented
6C3×C22⋊#95C211yesmaximal, characteristic, complemented
7#72127C211yesmaximal, characteristic, complemented
8#71544C211yesmaximal, characteristic, complemented
9#69428C212yesmaximal, complemented
10#69428C212yesmaximal, complemented
11#69427C212yesmaximal, complemented
12#14717—31nomaximal, Sylow
13C25×D3C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×Dic3C2211yescharacteristic
16C23×Dic6C2211yescharacteristic, complemented
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×(C2×D3)⋊C4—24no—
22C22×(C2×D3)⋊C4—28no—
23C22×(C2×D3)⋊C4C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×C4⋊Dic3C2211yescharacteristic, complemented
30C22×Dic3⋊C4C2211yescharacteristic, complemented
31C22×Dic3⋊C4C2211yescharacteristic, complemented
32C2×#878—24no—
33C2×#878—24no—
34C2×#878—24no—
35C2×C3×#95C2212yescomplemented
36C2×C3×#95C2212yescomplemented
37C2×C3⋊#95C2212yescomplemented
38C2×C3⋊#95C2212yescomplemented
39C2×C3⋊#95C2212yescomplemented
40C2×C3⋊#95C2212yescomplemented
41#4955—24no—
42#4955—24no—
43#4673—28no—
44C22×C22⋊Q8—31no—
45C23×C22⋊C4—31no—
46C2×#393—32no—
47C2×#379—31no—
48C2×#379—31no—
49#1439—32no—
50#1439—32no—
51#1439—32no—
52C22⋊#95—31no—
53C22⋊#95—31no—
54C22⋊#95D311yescharacteristic, complemented
55C25×C3C2311yescharacteristic
56C24×D3—22no—
57C24×D3—22no—
58C24×D3—24no—
59C24×D3—24no—
60C24×D3—22no—
61C24×D3—22no—
62C24×D3—22no—
63C24×D3—22no—
64C24×D3—42no—
65C24×D3—42no—
66C24×D3Q814yescomplemented
67C24×D3C2312yes—
68C23×C3×C4—22no—
69C23×C3×C4—24no—
70C23×C3×C4—22no—
71C23×C3×C4—22no—
72C23×C3×C4—42no—
73C23×C3×C4C2312yes—
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2312yes—
76C23×C3×C4C2311yescharacteristic
77C23×Dic3—22no—
78C23×Dic3—22no—
79C23×Dic3—24no—
80C23×Dic3—42no—
81C23×Dic3D414yes—
82C23×Dic3C2312yes—
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C22×Dic6—22no—
88C22×Dic6—22no—
89C22×Dic6—22no—
90C22×Dic6—24no—
91C22×Dic6—42no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4D414yes—
98C2×#217—22no—
99C2×#217—22no—
100C2×#217—22no—
101C2×#217—22no—
102C2×#217—22no—
103C2×#217D414yes—
104C2×(C2×D3)⋊C4—232no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—24no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—24no—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—42no—
119C2×(C2×D3)⋊C4—42no—
120C2×(C2×D3)⋊C4—42no—
121C2×(C2×D3)⋊C4—42no—
122C2×(C2×D3)⋊C4D418yes—
123C2×C4⋊Dic3—22no—
124C2×C4⋊Dic3—22no—
125C2×C4⋊Dic3—22no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C2×Dic3⋊C4—22no—
129C2×Dic3⋊C4—22no—
130C2×Dic3⋊C4—22no—
131C2×Dic3⋊C4—22no—
132#878—232no—
133C3×#95—24no—
134C3×#95—42no—
135C3⋊#95—24no—
136C3⋊#95—24no—
137C3⋊#95—42no—
138C3⋊#95—42no—
139C26—31no—
140C23×Q8—31no—
141C24×C4—31no—
142C24×C4C2×D311yescharacteristic
143C2×C22⋊Q8—64no—
144C2×C22⋊Q8—64no—
145C2×C22⋊Q8—64no—
146C22×C4⋊C4—31no—
147C22×C4⋊C4—31no—
148C22×C4⋊C4—31no—
149C22×C22⋊C4—31no—
150C22×C22⋊C4—32no—
151C22×C22⋊C4—31no—
152C22×C22⋊C4—32no—
153C22×C22⋊C4—32no—
154C22×C22⋊C4—32no—
155C22×C22⋊C4—32no—
156C22×C22⋊C4—32no—
157C22×C22⋊C4—68no—
158C22×C22⋊C4—64no—
159C22×C22⋊C4C2×D311yescharacteristic
160C22×C22⋊C4C2×D311yescharacteristic
161#393—68no—
162#379—64no—
163#379—64no—
164C2×#95—32no—
165C2×#95—32no—
166C2×#95—32no—
167C2×#95—32no—
168C2×#95C2×D312yescomplemented
169C2×#95C2×D312yescomplemented
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3C2×D412yes—
175C24×C3C2×D412yes—
176C24×C3C2×D412yes—
177C24×C3C2×Q812yes—
178C24×C3#4112yes—
179C24×C3#4112yes—
180C24×C3#4112yes—
181C24×C3C2411yescharacteristic
182C23×D3—28no—
183C23×D3—216no—
184C23×D3—28no—
185C23×D3—28no—
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—22no—
189C23×D3—22no—
190C23×D3—22no—
191C23×D3—22no—
192C23×D3—22no—
193C23×D3—22no—
194C23×D3—22no—
195C23×D3—22no—
196C23×D3—22no—
197C23×D3—22no—
198C23×D3—216no—
199C23×D3—28no—
200C23×D3—28no—
201C23×D3—48no—
202C23×D3—48no—
203C23×D3—48no—
204C23×D3—48no—
205C23×D3—48no—
206C23×D3—48no—
207C23×D3—48no—
208C23×D3—48no—
209C23×D3—48no—
210C23×D3—44no—
211C23×D3—44no—
212C23×D3—48no—
213C23×D3—44no—
214C23×D3—44no—
215C23×D3—44no—
216C23×D3—44no—
217C23×D3C2×D414yes—
218C23×D3C2×Q814yes—
219C23×D3#4114yes—
220C22×C3×C4—28no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—48no—
243C22×C3×C4—48no—
244C22×C3×C4—44no—
245C22×C3×C4—44no—
246C22×C3×C4C2×D412yes—
247C22×C3×C4C2×D412yes—
248C22×C3×C4C2×D414yes—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—22no—
252C22×Dic3—28no—
253C22×Dic3—22no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—28no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—44no—
274C22×Dic3—48no—
275C22×Dic3—48no—
276C22×Dic3C2×D412yes—
277C22×Dic3C2×D412yes—
278C22×Dic3C2×D412yes—
279C22×Dic3C2×D414yes—
280C22×Dic3C2×D412yes—
281C2×Dic6—28no—
282C2×Dic6—48no—
283C2×Dic6—48no—
284C2×Dic6—44no—
285C2×Dic6—44no—
286C3×C22⋊C4—28no—
287C3×C22⋊C4—44no—
288#217—28no—
289#217—44no—
290(C2×D3)⋊C4—216no—
291(C2×D3)⋊C4—216no—
292(C2×D3)⋊C4—48no—
293(C2×D3)⋊C4—48no—
294(C2×D3)⋊C4—48no—
295(C2×D3)⋊C4—48no—
296C4⋊Dic3—28no—
297Dic3⋊C4—28no—
298Dic3⋊C4—28no—
299C25—32no—
300C25—34no—
301C25—64no—
302C25—64no—
303C25—62no—
304C25—62no—
305C25—62no—
306C25—62no—
307C25—62no—
308C25—62no—
309C25—122no—
310C25—122no—
311C25C22×D311yescharacteristic
312C22×Q8—62no—
313C22×Q8—62no—
314C22×Q8—64no—
315C22×Q8—62no—
316C22×Q8—122no—
317C23×C4—22no—
318C23×C4—24no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—34no—
326C23×C4—32no—
327C23×C4—42no—
328C23×C4—64no—
329C23×C4—62no—
330C23×C4—62no—
331C23×C4—122no—
332C23×C4C22×D312yes—
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D312yes—
336C22⋊Q8—632no—
337C2×C4⋊C4—62no—
338C2×C4⋊C4—62no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—62no—
341C2×C4⋊C4—62no—
342C2×C4⋊C4—62no—
343C2×C4⋊C4—62no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4—62no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—34no—
352C2×C22⋊C4—38no—
353C2×C22⋊C4—64no—
354C2×C22⋊C4—64no—
355C2×C22⋊C4—64no—
356C2×C22⋊C4—64no—
357C2×C22⋊C4—632no—
358C2×C22⋊C4—62no—
359C2×C22⋊C4—62no—
360C2×C22⋊C4—64no—
361C2×C22⋊C4—64no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—64no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—64no—
366C2×C22⋊C4—64no—
367C2×C22⋊C4—62no—
368C2×C22⋊C4—62no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—64no—
371C2×C22⋊C4—64no—
372C2×C22⋊C4—122no—
373C2×C22⋊C4—122no—
374C2×C22⋊C4—122no—
375C2×C22⋊C4—122no—
376C2×C22⋊C4D1214yes—
377#95—24no—
378#95—42no—
379#95—64no—
380#95—64no—
381#95—122no—
382#95—122no—
383C23×C3—22no—
384C23×C3—24no—
385C23×C3—22no—
386C23×C3—24no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—24no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3#12014yes—
400C23×C3C22⋊Q814yes—
401C23×C3C22⋊Q814yes—
402C23×C3C22⋊Q814yes—
403C23×C3#12414yes—
404C23×C3#12414yes—
405C23×C3#12414yes—
406C23×C3C22×D411yescharacteristic
407C23×C3C22×D411yescharacteristic
408C23×C3C22×D412yes—
409C23×C3C22×D411yescharacteristic
410C23×C3C22×Q811yescharacteristic
411C23×C3C2×#4111yescharacteristic
412C23×C3C2×#4111yescharacteristic
413C23×C3C2×#4111yescharacteristic
414C23×C3C2×#4112yes—
415C23×C3H(5,𝔽2)12yes—
416C23×C3H(5,𝔽2)12yes—
417C22×D3—232no—
418C22×D3—24no—
419C22×D3—24no—
420C22×D3—24no—
421C22×D3—24no—
422C22×D3—24no—
423C22×D3—24no—
424C22×D3—24no—
425C22×D3—24no—
426C22×D3—24no—
427C22×D3—24no—
428C22×D3—24no—
429C22×D3—24no—
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—24no—
433C22×D3—24no—
434C22×D3—24no—
435C22×D3—24no—
436C22×D3—432no—
437C22×D3—432no—
438C22×D3—416no—
439C22×D3—416no—
440C22×D3—416no—
441C22×D3—416no—
442C22×D3—416no—
443C22×D3—432no—
444C22×D3—432no—
445C22×D3—42no—
446C22×D3—42no—
447C22×D3—42no—
448C22×D3—42no—
449C22×D3—42no—
450C22×D3—42no—
451C22×D3—42no—
452C22×D3—42no—
453C22×D3—42no—
454C22×D3—42no—
455C22×D3—42no—
456C22×D3—42no—
457C22×D3—42no—
458C22×D3—42no—
459C22×D3—42no—
460C22×D3—42no—
461C22×D3—416no—
462C22×D3C22⋊Q818yescomplemented
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—416no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—42no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4—42no—
479C2×C3×C4—42no—
480C2×C3×C4—42no—
481C2×C3×C4—42no—
482C2×C3×C4—42no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4—42no—
487C2×C3×C4—42no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—24no—
491C2×Dic3—24no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—24no—
498C2×Dic3—24no—
499C2×Dic3—416no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—42no—
505C2×Dic3—42no—
506C2×Dic3—42no—
507C2×Dic3—42no—
508C2×Dic3—42no—
509C2×Dic3—42no—
510C2×Dic3—42no—
511C2×Dic3—42no—
512C2×Dic3—42no—
513C2×Dic3—42no—
514C2×Dic3—42no—
515C2×Dic3#12014yes—
516Dic6—416no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—34no—
522C24—34no—
523C24—34no—
524C24—616no—
525C24—68no—
526C24—68no—
527C24—616no—
528C24—68no—
529C24—62no—
530C24—62no—
531C24—62no—
532C24—62no—
533C24—62no—
534C24—62no—
535C24—62no—
536C24—62no—
537C24—62no—
538C24—62no—
539C24—62no—
540C24—62no—
541C24—68no—
542C24—68no—
543C24—128no—
544C24—128no—
545C24—128no—
546C24—128no—
547C24—128no—
548C24—128no—
549C24—128no—
550C24—128no—
551C24—128no—
552C24—124no—
553C24—128no—
554C24—124no—
555C24—124no—
556C24—124no—
557C24—124no—
558C24—124no—
559C24C2×D1212yes—
560C24#23512yes—
561C24#23512yes—
562C24D3×D412yes—
563C24D3×D412yes—
564C24#23712yes—
565C24D3×Q812yes—
566C24C23×D311yescharacteristic
567C2×Q8—68no—
568C2×Q8—128no—
569C2×Q8—124no—
570C2×Q8—128no—
571C2×Q8—124no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
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—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—34no—
595C22×C4—32no—
596C22×C4—32no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—68no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—62no—
607C22×C4—68no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
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—62no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—124no—
628C22×C4—128no—
629C22×C4—128no—
630C22×C4C2×D1212yes—
631C22×C4C2×D1212yes—
632C22×C4D3×D414yes—
633C4⋊C4—68no—
634C4⋊C4—68no—
635C4⋊C4—68no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—616no—
639C22⋊C4—616no—
640C22⋊C4—68no—
641C22⋊C4—128no—
642C22⋊C4—128no—
643C22⋊C4—128no—
644C22⋊C4—128no—
645C22⋊C4—124no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—24no—
651C22×C3—24no—
652C22×C3—28no—
653C22×C3—28no—
654C22×C3—28no—
655C22×C3—28no—
656C22×C3#39318yescomplemented
657C22×C3C2×#12011yescharacteristic
658C22×C3C2×#12011yescharacteristic
659C22×C3C2×C22⋊Q811yescharacteristic
660C22×C3C2×C22⋊Q811yescharacteristic
661C22×C3C2×C22⋊Q811yescharacteristic
662C22×C3C2×C22⋊Q812yes—
663C22×C3#52511yescharacteristic
664C22×C3#52512yes—
665C22×C3C2×#12411yescharacteristic
666C22×C3C2×#12411yescharacteristic
667C22×C3C2×#12411yescharacteristic
668C22×C3#53411yescharacteristic
669C22×C3#53511yescharacteristic
670C22×C3#53812yes—
671C22×C3#54312yes—
672C22×C3D4212yes—
673C22×C3D4212yes—
674C22×C3#54612yes—
675C22×C3#54612yes—
676C22×C3#54612yes—
677C22×C3#54612yes—
678C22×C3#55112yes—
679C22×C3#55112yes—
680C2×D3—28no—
681C2×D3—28no—
682C2×D3—28no—
683C2×D3—464no—
684C2×D3—44no—
685C2×D3—44no—
686C2×D3—44no—
687C2×D3—44no—
688C2×D3—44no—
689C2×D3—44no—
690C2×D3—44no—
691C2×D3—44no—
692C2×D3—44no—
693C2×D3—44no—
694C2×D3—44no—
695C2×D3—44no—
696C3×C4—42no—
697C3×C4—42no—
698C3×C4—44no—
699C3×C4—82no—
700Dic3—24no—
701Dic3—42no—
702Dic3—42no—
703Dic3—42no—
704Dic3—82no—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—22no—
716C23—24no—
717C23—22no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—38no—
722C23—632no—
723C23—64no—
724C23—64no—
725C23—64no—
726C23—64no—
727C23—64no—
728C23—64no—
729C23—64no—
730C23—64no—
731C23—64no—
732C23—64no—
733C23—64no—
734C23—64no—
735C23—64no—
736C23—64no—
737C23—64no—
738C23—64no—
739C23—64no—
740C23—64no—
741C23—1232no—
742C23—1232no—
743C23—1216no—
744C23—1232no—
745C23—1216no—
746C23—1216no—
747C23—1216no—
748C23—1216no—
749C23—1232no—
750C23—122no—
751C23—122no—
752C23—1216no—
753C23—122no—
754C23—122no—
755C23—122no—
756C23—122no—
757C23—122no—
758C23—122no—
759C23—122no—
760C23—122no—
761C23—122no—
762C23—122no—
763C23—122no—
764C23—122no—
765C23—122no—
766C23—122no—
767C23#87514yes—
768C23#88214yes—
769C23#88514yes—
770C23#88514yes—
771C23#89614yes—
772C23#89614yes—
773C23#89714yes—
774C23C22×D1211yescharacteristic
775C23C2×#23511yescharacteristic
776C23C2×#23511yescharacteristic
777C23C2×D3×D411yescharacteristic
778C23C2×D3×D411yescharacteristic
779C23C2×D3×D412yes—
780C23C2×#23711yescharacteristic
781C23#100412yes—
782C23C2×D3×Q811yescharacteristic
783C23D3×#4112yes—
784C23#100912yes—
785Q8—1216no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—34no—
794C2×C4—416no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—64no—
815C2×C4—64no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—64no—
822C2×C4—64no—
823C2×C4—1216no—
824C2×C4—121no—
825C2×C4—121no—
826C2×C4—122no—
827C2×C4—122no—
828C2×C4—122no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—122no—
832C2×C4—122no—
833C2×C4—122no—
834C2×C4—122no—
835C2×C4—122no—
836C2×C4—122no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C3—28no—
840C2×C3C2×#39311yescharacteristic
841C2×C3#240311yescharacteristic
842C2×C3#240411yescharacteristic
843C2×C3#243511yescharacteristic
844C2×C3#243712yes—
845C2×C3#243712yes—
846C2×C3#247212yes—
847C2×C3#247212yes—
848C2×C3#256111yescharacteristic
849C2×C3#262611yescharacteristic
850C2×C3#284811yescharacteristic
851D3—48no—
852C22—24no—
853C22—28no—
854C22—24no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—24no—
859C22—28no—
860C22—28no—
861C22—28no—
862C22—68no—
863C22—68no—
864C22—68no—
865C22—1264no—
866C22—124no—
867C22—124no—
868C22—124no—
869C22—124no—
870C22—124no—
871C22—124no—
872C22—124no—
873C22—124no—
874C22—124no—
875C22—124no—
876C22—124no—
877C22—124no—
878C22#467318yescomplemented
879C22C2×#87511yescharacteristic
880C22C2×#88211yescharacteristic
881C22#549012yes—
882C22C2×#88511yescharacteristic
883C22C2×#88511yescharacteristic
884C22C2×#89611yescharacteristic
885C22C2×#89611yescharacteristic
886C22C2×#89711yescharacteristic
887C22#552712yes—
888C22#554712yes—
889C22D4×D1212yes—
890C22#555412yes—
891C22#556012yes—
892C22D3×#12011yescharacteristic
893C22#559112yes—
894C22#559211yescharacteristic
895C22#560912yes—
896C22#561012yes—
897C22D3×C22⋊Q812yes—
898C22#563412yes—
899C22#565311yescharacteristic
900C22#565611yescharacteristic
901C22#565812yes—
902C4—44no—
903C4—42no—
904C4—42no—
905C4—64no—
906C4—82no—
907C4—122no—
908C4—122no—
909C4—122no—
910C4—242no—
911C3#1471711yescharacteristic, complemented, Sylow
912C2—28no—
913C2—128no—
914C2C2×#467311yescharacteristic
915C2#7359412yes—
916C2#7382711yescharacteristic
917C2#7389612yes—
918C2#7413211yescharacteristic
919C2#7441312yes—
920C2#7462111yescharacteristic
921C2#7465511yescharacteristic
922C2#7472712yes—
923C2#7488411yescharacteristic
924C2#7488511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C22⋊#95C2
prime radicalC25×D3C22
hypercenterC22⋊#95D3
hypocenterC3#14717
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×#878C2semidirect
5. C2×#4673C2semidirect
6. C3×C22⋊#95C2semidirect
7. #72127C2semidirect
8. #71544C2semidirect
9. #69428C2semidirect
10. #69428C2semidirect
11. #69427C2semidirect
16. C23×Dic6C22semidirect
29. C22×C4⋊Dic3C22semidirect
30. C22×Dic3⋊C4C22semidirect
31. C22×Dic3⋊C4C22semidirect
35. C2×C3×#95C22semidirect
36. C2×C3×#95C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. C2×C3⋊#95C22semidirect
40. C2×C3⋊#95C22semidirect
54. C22⋊#95D3semidirect
66. C24×D3Q8semidirect
168. C2×#95C2×D3semidirect
169. C2×#95C2×D3semidirect
462. C22×D3C22⋊Q8semidirect
656. C22×C3#393semidirect
878. C22#4673semidirect
911. C3#14717semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D3)⋊C42
C22×#8782
C2×#49552
C2×#46732
C3×C22⋊#952
#721272
#715442
#694282
#694272
#147173