Finite Group Databasebeta

← #10968218

Subgroups — #10968218

Order 768.

2930 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic
2C22×#924C211yesmaximal, characteristic, complemented
3#84043C212yesmaximal
4#84031C212yesmaximal, complemented
5C2×#5212C211yesmaximal, characteristic, complemented
6#82387C214yesmaximal, complemented
7#82385C214yesmaximal, complemented
8#82374C212yesmaximal, complemented
9#82353C214yesmaximal, complemented
10#82349C212yesmaximal, complemented
11#82183C212yesmaximal, complemented
12#82117C212yesmaximal, complemented
13#82095C212yesmaximal, complemented
14#82075C212yesmaximal, complemented
15#35010—31nomaximal, Sylow
16C23×C3×D4C2211yescharacteristic
17C24×C3×C4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×Dic6C2211yescharacteristic, complemented
20C2×C3×C4×D4—28no—
21C2×C3×C4×D4C2212yes—
22C2×C3×C4×D4C2212yes—
23C2×C3×C4×D4C2212yes—
24C2×C3×C4×D4C2212yes—
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C42C2211yescharacteristic
29C22×#217C2212yes—
30C22×#217C2212yes—
31C22×C4⋊Dic3C2211yescharacteristic, complemented
32C22×C4⋊Dic3C2212yescomplemented
33C2×#924—28no—
34C2×#924C2212yes—
35C2×#924C2212yes—
36C2×#924C2212yescomplemented
37C2×#924C2212yescomplemented
38C2×#924C2214yescomplemented
39C22×Dic3⋊C4C2212yescomplemented
40#5247C2214yes—
41#5220C2214yes—
42#5220C2218yes—
43#5220C2214yes—
44#5212C2212yes—
45#5212C2212yes—
46#5212C2212yescomplemented
47#5212C2212yescomplemented
48#5212C2214yescomplemented
49#5211C2214yes—
50#5210C2214yes—
51#5210C2214yes—
52#5210C2218yescomplemented
53C2×C3⋊#95C2212yescomplemented
54#4986C2214yescomplemented
55#4982C2218yescomplemented
56#4979C2214yescomplemented
57#4949C2214yescomplemented
58#4948C2218yescomplemented
59#4947C2214yescomplemented
60#4946C2214yescomplemented
61#4946C2214yescomplemented
62#4942C2218yescomplemented
63#4933C2218yescomplemented
64#4929C2214yescomplemented
65#4928C2214yescomplemented
66C22×C22⋊Q8—31no—
67C22×C4×D4D311yescharacteristic
68#2855—32no—
69#2848—32no—
70#2627—32no—
71#2626—32no—
72#2579—34no—
73#2564—34no—
74#2487—32no—
75#2417—34no—
76#2409—32no—
77#2315—32no—
78#2308—32no—
79C2×#380—31no—
80C25×C3C2311yescharacteristic
81C25×C3C2311yescharacteristic
82C22×C3×D4—24no—
83C22×C3×D4—24no—
84C22×C3×D4Q818yescomplemented
85C22×C3×D4C2312yes—
86C22×C3×D4C2312yes—
87C23×C3×C4—24no—
88C23×C3×C4—44no—
89C23×C3×C4—44no—
90C23×C3×C4D418yes—
91C23×C3×C4C2312yes—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2312yes—
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×Dic3C2312yes—
103C23×Dic3C2314yes—
104C23×Dic3C2312yes—
105C22×Dic6—24no—
106C22×Dic6—44no—
107C22×Dic6C2312yes—
108C22×Dic6C2312yes—
109C3×C4×D4—28no—
110C3×C4×D4—28no—
111C3×C4×D4—28no—
112C3×C4×D4—28no—
113C2×C3×C4⋊C4—24no—
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C4⋊C4C2312yes—
116C2×C3×C22⋊C4—24no—
117C2×C3×C22⋊C4—24no—
118C2×C3×C22⋊C4C2312yes—
119C2×C3×C22⋊C4C2312yes—
120C2×C3×C22⋊C4C2312yes—
121C2×C3×C22⋊C4C2312yes—
122C2×C3×C42—24no—
123C2×C3×C42C2312yes—
124C2×C3×C42C2312yes—
125C2×#217—28no—
126C2×#217—28no—
127C2×#217C2314yes—
128C2×#217C2314yes—
129C2×#217C2314yes—
130C2×#217C2314yes—
131C2×#217C2318yes—
132C2×#217C2318yes—
133C2×C4⋊Dic3—24no—
134C2×C4⋊Dic3—44no—
135C2×C4⋊Dic3C2312yes—
136C2×C4⋊Dic3C2314yes—
137C2×C4⋊Dic3C2312yes—
138C2×C4⋊Dic3C2314yes—
139#924—28no—
140#924—28no—
141#924—28no—
142#924—28no—
143#924—48no—
144C2×Dic3⋊C4—28no—
145C2×Dic3⋊C4C2314yes—
146C2×Dic3⋊C4C2314yes—
147C2×Dic3⋊C4C2318yes—
148C2×Dic3⋊C4C2318yes—
149C3⋊#95C2318yes—
150C3⋊#95C2318yes—
151C3⋊#95C2318yes—
152C3⋊#95C2314yes—
153C3⋊#95C2318yes—
154C3⋊#95C2314yes—
155C23×Q8—31no—
156C23×D4C2×D311yescharacteristic
157C24×C4C2×D311yescharacteristic
158C24×C4C2×D311yescharacteristic
159C2×C22⋊Q8—32no—
160C2×C22⋊Q8—32no—
161C2×C22⋊Q8—32no—
162C2×C22⋊Q8—32no—
163C2×C22⋊Q8—34no—
164C2×C22⋊Q8—68no—
165C2×C4×D4—28no—
166C2×C4×D4C2×D312yes—
167C2×C4×D4C2×D312yes—
168C2×C4×D4C2×D312yes—
169C2×C4×D4C2×D312yes—
170C22×C4⋊C4—32no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—32no—
173C22×C4⋊C4C2×D311yescharacteristic
174C22×C22⋊C4—32no—
175C22×C22⋊C4—32no—
176C22×C22⋊C4C2×D311yescharacteristic
177C22×C22⋊C4C2×D311yescharacteristic
178C22×C42C2×D311yescharacteristic
179#400—34no—
180#399—34no—
181#398—38no—
182#396—38no—
183#395—34no—
184#393—34no—
185#391—34no—
186#389—34no—
187#387—38no—
188#386—38no—
189#386—34no—
190#386—34no—
191#385—38no—
192#385—34no—
193#385—34no—
194#385—34no—
195#385—34no—
196#381—34no—
197#380—32no—
198#380—32no—
199#380—34no—
200#380—32no—
201#380—32no—
202#380—38no—
203#379—34no—
204C2×#95—32no—
205C24×C3—22no—
206C24×C3—22no—
207C24×C3—42no—
208C24×C3—42no—
209C24×C3—42no—
210C24×C3—42no—
211C24×C3C2×D414yes—
212C24×C3C2×Q814yes—
213C24×C3C2×Q814yescomplemented
214C24×C3#4114yes—
215C24×C3C2412yes—
216C24×C3C2411yescharacteristic
217C24×C3C2411yescharacteristic
218C24×C3C2411yescharacteristic
219C2×C3×D4—232no—
220C2×C3×D4—24no—
221C2×C3×D4—24no—
222C2×C3×D4—24no—
223C2×C3×D4—24no—
224C2×C3×D4C2×Q818yes—
225C2×C3×D4C2×Q818yescomplemented
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—24no—
229C22×C3×C4—24no—
230C22×C3×C4—24no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—24no—
234C22×C3×C4—24no—
235C22×C3×C4—28no—
236C22×C3×C4—416no—
237C22×C3×C4—42no—
238C22×C3×C4—42no—
239C22×C3×C4—42no—
240C22×C3×C4—44no—
241C22×C3×C4—42no—
242C22×C3×C4—42no—
243C22×C3×C4—416no—
244C22×C3×C4C2×D414yes—
245C22×C3×C4C2×D414yes—
246C22×C3×C4C2×D414yes—
247C22×C3×C4C2×D414yes—
248C22×C3×C4C2×D414yes—
249C22×C3×C4C2×D414yes—
250C22×C3×C4C2×Q814yescomplemented
251C22×C3×C4C2412yes—
252C22×C3×C4C2412yes—
253C22×C3×C4C2411yescharacteristic
254C22×C3×C4C2411yescharacteristic
255C22×C3×C4C2411yescharacteristic
256C22×C3×C4C2412yes—
257C22×C3×C4C2411yescharacteristic
258C22×Dic3—24no—
259C22×Dic3—24no—
260C22×Dic3—28no—
261C22×Dic3—44no—
262C22×Dic3—44no—
263C22×Dic3—44no—
264C22×Dic3—44no—
265C22×Dic3C2418yes—
266C22×Dic3C2414yes—
267C22×Dic3C2414yes—
268C2×Dic6—24no—
269C2×Dic6—24no—
270C2×Dic6—28no—
271C2×Dic6—44no—
272C2×Dic6—416no—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—24no—
275C3×C22⋊C4—24no—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—24no—
278C3×C22⋊C4—24no—
279C3×C42—24no—
280C3×C42—24no—
281#217—28no—
282#217—28no—
283#217—28no—
284#217—28no—
285#217—48no—
286#217—48no—
287C4⋊Dic3—24no—
288C4⋊Dic3—24no—
289C4⋊Dic3—28no—
290C4⋊Dic3—44no—
291Dic3⋊C4—28no—
292Dic3⋊C4—28no—
293Dic3⋊C4—48no—
294Dic3⋊C4—48no—
295C25C22×D311yescharacteristic
296C25C22×D311yescharacteristic
297C22×Q8—32no—
298C22×Q8—32no—
299C22×Q8—64no—
300C22×Q8—124no—
301C22×D4—24no—
302C22×D4—24no—
303C22×D4Dic618yescomplemented
304C22×D4C22×D312yes—
305C22×D4C22×D312yes—
306C23×C4—24no—
307C23×C4—32no—
308C23×C4—32no—
309C23×C4—34no—
310C23×C4—44no—
311C23×C4—44no—
312C23×C4#6718yes—
313C23×C4C22×D312yes—
314C23×C4C22×D311yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318C23×C4C22×D311yescharacteristic
319C23×C4C22×D311yescharacteristic
320C23×C4C22×D312yes—
321C23×C4C22×D311yescharacteristic
322C23×C4C22×D311yescharacteristic
323C23×C4C22×D311yescharacteristic
324C22⋊Q8—68no—
325C22⋊Q8—68no—
326C22⋊Q8—68no—
327C22⋊Q8—68no—
328C22⋊Q8—128no—
329C4×D4—28no—
330C4×D4—28no—
331C4×D4—28no—
332C4×D4—28no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—32no—
335C2×C4⋊C4—34no—
336C2×C4⋊C4—34no—
337C2×C4⋊C4—32no—
338C2×C4⋊C4—34no—
339C2×C4⋊C4—34no—
340C2×C4⋊C4—38no—
341C2×C4⋊C4—38no—
342C2×C4⋊C4—68no—
343C2×C4⋊C4—64no—
344C2×C4⋊C4—124no—
345C2×C4⋊C4C22×D312yes—
346C2×C4⋊C4C22×D312yes—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—34no—
350C2×C22⋊C4—34no—
351C2×C22⋊C4—34no—
352C2×C22⋊C4—34no—
353C2×C22⋊C4—38no—
354C2×C22⋊C4—38no—
355C2×C22⋊C4—68no—
356C2×C22⋊C4—68no—
357C2×C22⋊C4C22×D312yes—
358C2×C22⋊C4C22×D312yes—
359C2×C22⋊C4C22×D312yes—
360C2×C22⋊C4C22×D312yes—
361C2×C42—24no—
362C2×C42C22×D312yes—
363C2×C42C22×D312yes—
364#95—34no—
365#95—34no—
366#95—38no—
367#95—38no—
368#95—38no—
369#95—38no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—28no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—44no—
382C23×C3—44no—
383C23×C3—48no—
384C23×C3—48no—
385C23×C3—48no—
386C23×C3—44no—
387C23×C3—44no—
388C23×C3—48no—
389C23×C3C22⋊Q8116yescomplemented
390C23×C3C22×D412yes—
391C23×C3C22×D412yes—
392C23×C3C22×D412yes—
393C23×C3C22×Q814yes—
394C23×C3C22×Q812yes—
395C23×C3C22×Q812yes—
396C23×C3C22×Q812yes—
397C23×C3C2×#4112yes—
398C23×C3C2×#4112yes—
399C23×C3C2×#4112yes—
400C23×C3C2511yescharacteristic
401C3×D4—216no—
402C3×D4—216no—
403C2×C3×C4—28no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—28no—
410C2×C3×C4—28no—
411C2×C3×C4—28no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—44no—
417C2×C3×C4—44no—
418C2×C3×C4—44no—
419C2×C3×C4—48no—
420C2×C3×C4—44no—
421C2×C3×C4—44no—
422C2×C3×C4—48no—
423C2×C3×C4C22×D412yes—
424C2×C3×C4C22×D412yes—
425C2×C3×C4C22×D412yes—
426C2×C3×C4C22×D412yes—
427C2×C3×C4C22×Q814yes—
428C2×C3×C4H(5,𝔽2)14yes—
429C2×Dic3—24no—
430C2×Dic3—24no—
431C2×Dic3—28no—
432C2×Dic3—28no—
433C2×Dic3—28no—
434C2×Dic3—28no—
435C2×Dic3—28no—
436C2×Dic3—48no—
437C2×Dic3—48no—
438C2×Dic3—88no—
439Dic6—48no—
440Dic6—48no—
441C24—22no—
442C24—22no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24C2×Dic614yes—
448C24C2×Dic614yescomplemented
449C24#23514yes—
450C24C2×#6714yes—
451C24C23×D312yes—
452C24C23×D311yescharacteristic
453C24C23×D311yescharacteristic
454C24C23×D311yescharacteristic
455C2×Q8—68no—
456C2×Q8—64no—
457C2×Q8—64no—
458C2×Q8—124no—
459C2×Q8—1216no—
460C2×D4—232no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—24no—
465C2×D4C2×Dic618yes—
466C2×D4C2×Dic618yescomplemented
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—28no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—38no—
478C22×C4—34no—
479C22×C4—34no—
480C22×C4—416no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—44no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—416no—
488C22×C4—64no—
489C22×C4—64no—
490C22×C4—68no—
491C22×C4—124no—
492C22×C4—124no—
493C22×C4—124no—
494C22×C4—124no—
495C22×C4C2×Dic614yescomplemented
496C22×C4C2×#6714yes—
497C22×C4C2×#6714yes—
498C22×C4C2×#6714yes—
499C22×C4C2×#6714yes—
500C22×C4C2×#6714yes—
501C22×C4C2×#6714yes—
502C22×C4C23×D312yes—
503C22×C4C23×D312yes—
504C22×C4C23×D312yes—
505C22×C4C23×D311yescharacteristic
506C22×C4C23×D311yescharacteristic
507C22×C4C23×D311yescharacteristic
508C22×C4C23×D311yescharacteristic
509C4⋊C4—24no—
510C4⋊C4—24no—
511C4⋊C4—68no—
512C4⋊C4—68no—
513C4⋊C4—68no—
514C4⋊C4—64no—
515C4⋊C4—64no—
516C4⋊C4—124no—
517C4⋊C4—128no—
518C4⋊C4—128no—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—24no—
523C22⋊C4—68no—
524C22⋊C4—68no—
525C22⋊C4—68no—
526C22⋊C4—68no—
527C22⋊C4—128no—
528C22⋊C4—128no—
529C42—24no—
530C42—24no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—24no—
538C22×C3—24no—
539C22×C3—24no—
540C22×C3—24no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—28no—
545C22×C3—416no—
546C22×C3—416no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—44no—
550C22×C3C2×C22⋊Q814yes—
551C22×C3C2×C22⋊Q814yes—
552C22×C3C2×C22⋊Q814yes—
553C22×C3C23×D411yescharacteristic
554C22×C3C23×Q811yescharacteristic
555C22×C3C22×#4111yescharacteristic
556C22×C3C2×H(5,𝔽2)12yes—
557C22×C3#58512yes—
558C3×C4—24no—
559C3×C4—22no—
560C3×C4—22no—
561C3×C4—22no—
562C3×C4—42no—
563C3×C4—42no—
564C3×C4#53414yes—
565Dic3—44no—
566Dic3—44no—
567Dic3—48no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—24no—
576C23—24no—
577C23—22no—
578C23—28no—
579C23—44no—
580C23—48no—
581C23—48no—
582C23—48no—
583C23—44no—
584C23—44no—
585C23—48no—
586C23—44no—
587C23#924116yescomplemented
588C23C22×Dic614yes—
589C23C22×Dic612yes—
590C23C22×Dic612yes—
591C23C22×Dic612yes—
592C23C2×#23512yes—
593C23C2×#23512yes—
594C23C2×#23512yes—
595C23C22×#6712yes—
596C23C22×#6712yes—
597C23C22×#6712yes—
598C23C24×D311yescharacteristic
599Q8—128no—
600Q8—128no—
601D4—216no—
602D4—216no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—28no—
609C2×C4—28no—
610C2×C4—28no—
611C2×C4—28no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—48no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—48no—
623C2×C4—68no—
624C2×C4—68no—
625C2×C4—68no—
626C2×C4—68no—
627C2×C4—68no—
628C2×C4—64no—
629C2×C4—64no—
630C2×C4—128no—
631C2×C4—128no—
632C2×C4—248no—
633C2×C4C22×Dic614yes—
634C2×C4#100414yes—
635C2×C4C22×#6712yes—
636C2×C4C22×#6712yes—
637C2×C4C22×#6712yes—
638C2×C4C22×#6712yes—
639C2×C3—24no—
640C2×C3—24no—
641C2×C3—24no—
642C2×C3—44no—
643C2×C3C22×C22⋊Q811yescharacteristic
644C2×C3C2×#53411yescharacteristic
645C2×C3#344911yescharacteristic
646C2×C3#350112yes—
647C2×C3#350512yes—
648C22—24no—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22—24no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—28no—
661C22—24no—
662C22—416no—
663C22—416no—
664C22—44no—
665C22—42no—
666C22—42no—
667C22C2×#92414yes—
668C22C2×#92414yes—
669C22C2×#92414yes—
670C22C23×Dic611yescharacteristic
671C22C22×#23511yescharacteristic
672C22C2×#100412yes—
673C22#596412yes—
674C22C23×#6711yescharacteristic
675C4—24no—
676C4—22no—
677C4—22no—
678C4—22no—
679C4—42no—
680C4—42no—
681C4—128no—
682C4—124no—
683C4—124no—
684C4#580414yes—
685C3#3501011yescharacteristic, complemented, Sylow
686C2—24no—
687C2—24no—
688C2—24no—
689C2—44no—
690C2#8576612yes—
691C2#8578712yes—
692C2C22×#92411yescharacteristic
693C2C2×#580411yescharacteristic
694C2#8726811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC22×C3×C4×D4C2
prime radicalC23×C3×D4C22
hypercenterC22×C4×D4D3
hypocenterC3#35010
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#924C2semidirect
4. #84031C2semidirect
5. C2×#5212C2semidirect
6. #82387C2semidirect
7. #82385C2semidirect
8. #82374C2semidirect
9. #82353C2semidirect
10. #82349C2semidirect
11. #82183C2semidirect
12. #82117C2semidirect
13. #82095C2semidirect
14. #82075C2semidirect
19. C23×Dic6C22semidirect
31. C22×C4⋊Dic3C22semidirect
32. C22×C4⋊Dic3C22semidirect
36. C2×#924C22semidirect
37. C2×#924C22semidirect
38. C2×#924C22semidirect
39. C22×Dic3⋊C4C22semidirect
46. #5212C22semidirect
47. #5212C22semidirect
48. #5212C22semidirect
52. #5210C22semidirect
53. C2×C3⋊#95C22semidirect
54. #4986C22semidirect
55. #4982C22semidirect
56. #4979C22semidirect
57. #4949C22semidirect
58. #4948C22semidirect
59. #4947C22semidirect
60. #4946C22semidirect
61. #4946C22semidirect
62. #4942C22semidirect
63. #4933C22semidirect
64. #4929C22semidirect
65. #4928C22semidirect
84. C22×C3×D4Q8semidirect
213. C24×C3C2×Q8semidirect
225. C2×C3×D4C2×Q8semidirect
250. C22×C3×C4C2×Q8semidirect
303. C22×D4Dic6semidirect
389. C23×C3C22⋊Q8semidirect
448. C24C2×Dic6semidirect
466. C2×D4C2×Dic6semidirect
495. C22×C4C2×Dic6semidirect
587. C23#924semidirect
685. C3#35010semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C22×#9242
#840432
#840312
C2×#52122
#823872
#823852
#823742
#823532
#823492
#821832
#821172
#820952
#820752
#350103