Finite Group Databasebeta

← #10719004

Subgroups — #10719004

Order 768.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#888C211yesmaximal, characteristic
2C2×C3×#389C211yesmaximal, characteristic
3C2×#4973C212yesmaximal
4C2×Dic3×C4⋊C4C211yesmaximal, characteristic
5#71566C212yesmaximal
6#71563C211yesmaximal, characteristic
7#71563C211yesmaximal, characteristic
8#71535C211yesmaximal, characteristic
9C4×C3⋊#95C211yesmaximal, characteristic
10#69424C212yesmaximal
11#69405C212yesmaximal
12#14053—31nomaximal, Sylow
13C23×Dic6C2212yes—
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C42C2211yescharacteristic
18C22×C4⋊Dic3C2211yescharacteristic
19C22×C4⋊Dic3C2211yescharacteristic
20C22×Dic3⋊C4C2212yes—
21C22×C4×Dic3C2212yes—
22C22×C4×Dic3C2211yescharacteristic
23C22×C4×Dic3C2211yescharacteristic
24C2×#888—24no—
25C2×#888—24no—
26C2×#888C418yescomplemented
27C3×#389—24no—
28C2×C3×#95C2212yes—
29C2×C3⋊#95C2212yes—
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40Dic3×C4⋊C4—24no—
41#4973—28no—
42C22×C4⋊Q8—31no—
43C2×#391—32no—
44C2×#389D311yescharacteristic
45C2×C4×C4⋊C4—31no—
46#1446—32no—
47#1441—32no—
48#1436—32no—
49C4⋊#95—31no—
50C4⋊#95—31no—
51C4⋊#95—31no—
52C4×#95—31no—
53C23×C3×C4C2312yes—
54C23×C3×C4C2311yescharacteristic
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×Dic3C2312yes—
59C23×Dic3C2311yescharacteristic
60C23×Dic3C2312yes—
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2311yescharacteristic
63C23×Dic3C2311yescharacteristic
64C22×Dic6—24no—
65C22×Dic6—24no—
66C22×Dic6—24no—
67C22×Dic6—24no—
68C22×Dic6—42no—
69C22×Dic6—42no—
70C22×Dic6C2×C418yes—
71C2×C3×C4⋊C4—24no—
72C2×C3×C4⋊C4—24no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—42no—
77C2×C3×C4⋊C4C2×C414yes—
78C2×C3×C4⋊C4D414yes—
79C2×C3×C4⋊C4D414yes—
80C2×C3×C42—22no—
81C2×C3×C42—22no—
82C2×C3×C42—22no—
83C2×C4⋊Dic3—22no—
84C2×C4⋊Dic3—22no—
85C2×C4⋊Dic3—22no—
86C2×C4⋊Dic3—22no—
87C2×C4⋊Dic3C2×C414yes—
88C2×C4⋊Dic3Q814yescomplemented
89C2×Dic3⋊C4—24no—
90C2×Dic3⋊C4—24no—
91C2×Dic3⋊C4C2×C418yes—
92C2×C4×Dic3—22no—
93C2×C4×Dic3—22no—
94C2×C4×Dic3—22no—
95C2×C4×Dic3—22no—
96C2×C4×Dic3—24no—
97C2×C4×Dic3—24no—
98C2×C4×Dic3—42no—
99C2×C4×Dic3C2×C414yes—
100C2×C4×Dic3Q814yescomplemented
101#888—232no—
102C3×#95—24no—
103C3⋊#95—24no—
104C3⋊#95—24no—
105C3⋊#95—24no—
106C3⋊#95—24no—
107C3⋊#95—22no—
108C3⋊#95—22no—
109C3⋊#95—24no—
110C3⋊#95—42no—
111C3⋊#95—42no—
112C3⋊#95D414yes—
113C3⋊#95Q814yescomplemented
114C23×Q8—32no—
115C2×C4⋊Q8—38no—
116C2×C4⋊Q8—64no—
117C2×C4⋊Q8—64no—
118C22×C4⋊C4—32no—
119C22×C4⋊C4—31no—
120C22×C4⋊C4—31no—
121C22×C4⋊C4C2×D311yescharacteristic
122C22×C4⋊C4C2×D312yes—
123C22×C4⋊C4C2×D311yescharacteristic
124C22×C42—31no—
125C22×C42—31no—
126C22×C42—32no—
127C22×C42C2×D311yescharacteristic
128#391—68no—
129#389—24no—
130C4×C4⋊C4—64no—
131C2×#95—31no—
132C2×#95—31no—
133C2×#95—31no—
134C2×#95—31no—
135C2×#95—32no—
136C2×#95—32no—
137C2×#95—32no—
138C2×#95—32no—
139C2×#95—32no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95C2×D312yes—
143C24×C3C2411yescharacteristic
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4C22×C414yes—
168C22×C3×C4C22×C412yes—
169C22×C3×C4C2×D414yes—
170C22×C3×C4C2×D412yes—
171C22×C3×C4C2×D412yes—
172C22×C3×C4C2×D414yes—
173C22×C3×C4C2×D412yes—
174C22×C3×C4C2×Q812yes—
175C22×C3×C4C2×Q812yes—
176C22×C3×C4C2×Q812yes—
177C22×C3×C4#4112yes—
178C22×C3×C4#4112yes—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—21no—
191C22×Dic3—21no—
192C22×Dic3—22no—
193C22×Dic3—22no—
194C22×Dic3—22no—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—22no—
200C22×Dic3—21no—
201C22×Dic3—22no—
202C22×Dic3—22no—
203C22×Dic3—21no—
204C22×Dic3—22no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—21no—
208C22×Dic3—22no—
209C22×Dic3C22×C414yes—
210C22×Dic3C22×C412yes—
211C22×Dic3C22×C412yes—
212C22×Dic3C2×D412yes—
213C22×Dic3C2×D412yes—
214C22×Dic3C2×Q812yes—
215C22×Dic3C2×Q814yes—
216C22×Dic3C2×Q812yes—
217C22×Dic3C2×Q812yes—
218C22×Dic3C2×Q812yes—
219C22×Dic3#4112yes—
220C22×Dic3#4112yes—
221C2×Dic6—216no—
222C2×Dic6—216no—
223C2×Dic6—48no—
224C2×Dic6—48no—
225C2×Dic6—48no—
226C2×Dic6—48no—
227C2×Dic6—48no—
228C3×C4⋊C4—48no—
229C3×C4⋊C4—44no—
230C3×C4⋊C4C22⋊C4116yes—
231C3×C42—44no—
232C4⋊Dic3—28no—
233C4⋊Dic3—28no—
234Dic3⋊C4—216no—
235C4×Dic3—28no—
236C4×Dic3—28no—
237C4×Dic3—48no—
238C22×Q8—38no—
239C22×Q8—64no—
240C22×Q8—64no—
241C22×Q8—64no—
242C22×Q8—64no—
243C22×Q8—122no—
244C22×Q8—122no—
245C23×C4—31no—
246C23×C4—31no—
247C23×C4—31no—
248C23×C4—32no—
249C23×C4—32no—
250C23×C4—31no—
251C23×C4C22×D312yes—
252C23×C4C22×D311yescharacteristic
253C23×C4C22×D311yescharacteristic
254C23×C4C22×D312yes—
255C23×C4C22×D311yescharacteristic
256C4⋊Q8—632no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—38no—
263C2×C4⋊C4—34no—
264C2×C4⋊C4—34no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—64no—
267C2×C4⋊C4—62no—
268C2×C4⋊C4—62no—
269C2×C4⋊C4—62no—
270C2×C4⋊C4—64no—
271C2×C4⋊C4—62no—
272C2×C4⋊C4C4×D314yes—
273C2×C4⋊C4D1214yes—
274C2×C4⋊C4#6714yes—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42—22no—
278C2×C42—34no—
279C2×C42—34no—
280C2×C42—62no—
281C2×C42—62no—
282C2×C42—62no—
283C2×C42—62no—
284C2×C42—64no—
285C2×C42—64no—
286C2×C42—122no—
287#95—24no—
288#95—34no—
289#95—34no—
290#95—62no—
291#95—62no—
292#95—64no—
293#95—64no—
294#95—64no—
295#95—64no—
296#95—64no—
297#95—122no—
298#95—122no—
299C23×C3C23×C411yescharacteristic
300C23×C3C22×D411yescharacteristic
301C23×C3C22×D411yescharacteristic
302C23×C3C22×D411yescharacteristic
303C23×C3C22×Q811yescharacteristic
304C23×C3C22×Q811yescharacteristic
305C23×C3C22×Q811yescharacteristic
306C23×C3C2×#4111yescharacteristic
307C23×C3C2×#4111yescharacteristic
308C23×C3C2×#4111yescharacteristic
309C23×C3C2×#4111yescharacteristic
310C23×C3H(5,𝔽2)11yescharacteristic
311C23×C3H(5,𝔽2)11yescharacteristic
312C23×C32−1+411yescharacteristic
313C23×C32−1+411yescharacteristic
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4—24no—
319C2×C3×C4—24no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4C2×C22⋊C418yes—
342C2×C3×C4C2×C22⋊C414yes—
343C2×C3×C4C4×Q814yes—
344C2×C3×C4C4×Q814yes—
345C2×C3×C4C22⋊Q814yes—
346C2×C3×C4C22⋊Q814yes—
347C2×C3×C4#12414yes—
348C2×C3×C4C4⋊Q814yes—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—24no—
368C2×Dic3—24no—
369C2×Dic3—24no—
370C2×Dic3—22no—
371C2×Dic3—24no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—24no—
375C2×Dic3—24no—
376C2×Dic3—42no—
377C2×Dic3—42no—
378C2×Dic3—42no—
379C2×Dic3—42no—
380C2×Dic3—42no—
381C2×Dic3—42no—
382C2×Dic3—42no—
383C2×Dic3—41no—
384C2×Dic3—41no—
385C2×Dic3—42no—
386C2×Dic3—41no—
387C2×Dic3—41no—
388C2×Dic3C4×D414yes—
389C2×Dic3C4×Q814yes—
390C2×Dic3C4⋊Q814yescomplemented
391Dic6—432no—
392C24C23×D311yescharacteristic
393C2×Q8—616no—
394C2×Q8—616no—
395C2×Q8—128no—
396C2×Q8—128no—
397C2×Q8—128no—
398C2×Q8—128no—
399C2×Q8—128no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—32no—
424C22×C4—32no—
425C22×C4—32no—
426C22×C4—32no—
427C22×C4—32no—
428C22×C4—32no—
429C22×C4—32no—
430C22×C4—32no—
431C22×C4—32no—
432C22×C4—34no—
433C22×C4—32no—
434C22×C4—34no—
435C22×C4—61no—
436C22×C4—61no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4—61no—
442C22×C4—61no—
443C22×C4—61no—
444C22×C4—61no—
445C22×C4—61no—
446C22×C4—61no—
447C22×C4—61no—
448C22×C4—62no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—62no—
452C22×C4—61no—
453C22×C4—62no—
454C22×C4—61no—
455C22×C4—62no—
456C22×C4—62no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—62no—
461C22×C4—62no—
462C22×C4—62no—
463C22×C4—62no—
464C22×C4—62no—
465C22×C4C2×C4×D314yes—
466C22×C4C2×C4×D312yes—
467C22×C4C2×D1214yes—
468C22×C4C2×D1212yes—
469C22×C4D3×D412yes—
470C22×C4#23712yes—
471C22×C4#23712yes—
472C22×C4D3×Q812yes—
473C22×C4D3×Q812yes—
474C22×C4D3×Q812yes—
475C22×C4C2×#6714yes—
476C22×C4C2×#6712yes—
477C4⋊C4—48no—
478C4⋊C4—44no—
479C4⋊C4—68no—
480C4⋊C4—616no—
481C4⋊C4—68no—
482C4⋊C4(C2×D3)⋊C4116yes—
483C42—44no—
484C42—68no—
485C42—68no—
486C42—128no—
487C22×C3C22×C22⋊C411yescharacteristic
488C22×C3C2×C4×D411yescharacteristic
489C22×C3C2×C4×Q811yescharacteristic
490C22×C3C2×C4×Q811yescharacteristic
491C22×C3C2×C4×Q811yescharacteristic
492C22×C3#51811yescharacteristic
493C22×C3#51911yescharacteristic
494C22×C3C2×C22⋊Q811yescharacteristic
495C22×C3C2×C22⋊Q811yescharacteristic
496C22×C3C2×#12411yescharacteristic
497C22×C3C2×C4⋊Q811yescharacteristic
498C22×C3C2×C4⋊Q811yescharacteristic
499C22×C3#53211yescharacteristic
500C22×C3#53311yescharacteristic
501C22×C3#53311yescharacteristic
502C22×C3#54211yescharacteristic
503C22×C3#54211yescharacteristic
504C22×C3#54411yescharacteristic
505C22×C3#54411yescharacteristic
506C22×C3D4211yescharacteristic
507C22×C3D4211yescharacteristic
508C22×C3#54611yescharacteristic
509C22×C3#54611yescharacteristic
510C22×C3#54711yescharacteristic
511C22×C3#54811yescharacteristic
512C22×C3#54811yescharacteristic
513C22×C3D4×Q811yescharacteristic
514C22×C3D4×Q811yescharacteristic
515C22×C3D4×Q811yescharacteristic
516C22×C3#55411yescharacteristic
517C22×C3#55411yescharacteristic
518C22×C3#55511yescharacteristic
519C22×C3#55611yescharacteristic
520C22×C3#55711yescharacteristic
521C22×C3Q8211yescharacteristic
522C3×C4—28no—
523C3×C4—42no—
524C3×C4—42no—
525C3×C4—82no—
526C3×C4#39118yescomplemented
527Dic3—24no—
528Dic3—24no—
529Dic3—24no—
530Dic3—44no—
531Dic3—42no—
532Dic3—44no—
533C23C22×C4×D311yescharacteristic
534C23C22×D1211yescharacteristic
535C23C2×D3×D411yescharacteristic
536C23C2×#23711yescharacteristic
537C23C2×#23711yescharacteristic
538C23#100411yescharacteristic
539C23C2×D3×Q811yescharacteristic
540C23C2×D3×Q811yescharacteristic
541C23C2×D3×Q811yescharacteristic
542C23#100711yescharacteristic
543C23D3×#4111yescharacteristic
544C23D3×#4111yescharacteristic
545C23#100911yescharacteristic
546C23#101011yescharacteristic
547C23C22×#6711yescharacteristic
548Q8—1232no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—34no—
562C2×C4—34no—
563C2×C4—34no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—64no—
599C2×C4—64no—
600C2×C4—62no—
601C2×C4—62no—
602C2×C4—64no—
603C2×C4—64no—
604C2×C4—64no—
605C2×C4—64no—
606C2×C4—121no—
607C2×C4—122no—
608C2×C4—122no—
609C2×C4—122no—
610C2×C4—122no—
611C2×C4—122no—
612C2×C4—121no—
613C2×C4—122no—
614C2×C4—121no—
615C2×C4—122no—
616C2×C4—122no—
617C2×C4—121no—
618C2×C4#88714yes—
619C2×C4#88714yes—
620C2×C4#89714yes—
621C2×C4#89714yes—
622C2×C4C2×(C2×D3)⋊C418yes—
623C2×C4C2×(C2×D3)⋊C414yes—
624C2×C4#93614yes—
625C2×C4#94414yes—
626C2×C3C2×#39111yescharacteristic
627C2×C3C4×C4⋊Q811yescharacteristic
628C2×C3#233111yescharacteristic
629C2×C3D4×C22⋊C411yescharacteristic
630C2×C3Q8×C22⋊C411yescharacteristic
631C2×C3#236511yescharacteristic
632C2×C3#236911yescharacteristic
633C2×C3#243911yescharacteristic
634C2×C3#244011yescharacteristic
635C2×C3#245111yescharacteristic
636C2×C3#245211yescharacteristic
637C2×C3#249111yescharacteristic
638C2×C3#249211yescharacteristic
639C2×C3#255011yescharacteristic
640C2×C3#255111yescharacteristic
641C22C2×#88711yescharacteristic
642C22C2×#88711yescharacteristic
643C22C2×#89711yescharacteristic
644C22C2×#89711yescharacteristic
645C22C4×D3×D411yescharacteristic
646C22#554511yescharacteristic
647C22D4×D1211yescharacteristic
648C22#555411yescharacteristic
649C22C4×D3×Q811yescharacteristic
650C22#557211yescharacteristic
651C22Q8×D1211yescharacteristic
652C22#557611yescharacteristic
653C22#559611yescharacteristic
654C22#560311yescharacteristic
655C22#561111yescharacteristic
656C22#561611yescharacteristic
657C22#562211yescharacteristic
658C22#563511yescharacteristic
659C22#564111yescharacteristic
660C22#564311yescharacteristic
661C22#568511yescharacteristic
662C22#568811yescharacteristic
663C22#568911yescharacteristic
664C22#569011yescharacteristic
665C22#572211yescharacteristic
666C22D3×C4⋊Q811yescharacteristic
667C22#572711yescharacteristic
668C22#572911yescharacteristic
669C22C22×(C2×D3)⋊C411yescharacteristic
670C22C2×#93611yescharacteristic
671C22D4×#6711yescharacteristic
672C22C2×#94411yescharacteristic
673C22Q8×#6711yescharacteristic
674C22#582911yescharacteristic
675C22#583111yescharacteristic
676C4—28no—
677C4—42no—
678C4—42no—
679C4—64no—
680C4—64no—
681C4—64no—
682C4—82no—
683C4—122no—
684C4—124no—
685C4—124no—
686C4#497318yescomplemented
687C3#1405311yescharacteristic, complemented, Sylow
688C2#7596711yescharacteristic
689C2#7597411yescharacteristic
690C2#7598611yescharacteristic
691C2#7598711yescharacteristic
692C2#7599711yescharacteristic
693C2#7599911yescharacteristic
694C2#7600911yescharacteristic
695C2#7601111yescharacteristic
696C2C2×#497311yescharacteristic
697C2D4×(C2×D3)⋊C411yescharacteristic
698C2Q8×(C2×D3)⋊C411yescharacteristic
699C2#8266211yescharacteristic
700C2#8277311yescharacteristic
701C2#8303611yescharacteristic
702C2#8324211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC2×C3×#389C2
socle, prime radical, cosocleC24×C3C24
hypercenterC2×#389D3
hypocenterC3#14053
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
26. C2×#888C4semidirect
88. C2×C4⋊Dic3Q8semidirect
100. C2×C4×Dic3Q8semidirect
113. C3⋊#95Q8semidirect
390. C2×Dic3C4⋊Q8semidirect
526. C3×C4#391semidirect
686. C4#4973semidirect
687. C3#14053semidirect

Maximal subgroups

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

subgroupindex
C22×#8882
C2×C3×#3892
C2×#49732
C2×Dic3×C4⋊C42
#715662
#715632
#715352
C4×C3⋊#952
#694242
#694052
#140533