Finite Group Databasebeta

← #10728134

Subgroups — #10728134

Order 768.

2254 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#386C211yesmaximal, characteristic
2C2×#5220C212yesmaximal
3C2×#5212C211yesmaximal, characteristic, complemented
4C22×C3⋊#95C211yesmaximal, characteristic, complemented
5C2×#4949C211yesmaximal, characteristic, complemented
6C2×#4942C212yesmaximal, complemented
7#71547C212yesmaximal, complemented
8#71546C211yesmaximal, characteristic, complemented
9#69423C211yesmaximal, characteristic, complemented
10#69421C212yesmaximal, complemented
11#69420C211yesmaximal, characteristic, complemented
12#14836—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C24×Dic3C2212yes—
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×#217C2212yes—
20C22×#217C2212yes—
21C22×#217C2212yes—
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×Dic3⋊C4C2212yes—
25C22×Dic3⋊C4C2212yes—
26C3×#386—24no—
27C2×C3×#95C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29#5220—28no—
30#5212—24no—
31C2×C3⋊#95—24no—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2211yescharacteristic
40#4949—24no—
41#4942—28no—
42C2×#399—31no—
43C2×#386—32no—
44C2×#386D311yescharacteristic
45C2×#380—31no—
46C2×#380—32no—
47C22×#95—31no—
48#1445—32no—
49#1445—31no—
50#1444—31no—
51#1439—31no—
52#1439—32no—
53C25×C3C2311yescharacteristic
54C25×C3C2311yescharacteristic
55C22×C3×D4—24no—
56C22×C3×D4—22no—
57C22×C3×D4—22no—
58C22×C3×D4—24no—
59C22×C3×D4Q814yes—
60C23×C3×C4—24no—
61C23×C3×C4—22no—
62C23×C3×C4—22no—
63C23×C3×C4—42no—
64C23×C3×C4D414yes—
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×Dic3—24no—
71C23×Dic3—24no—
72C23×Dic3—24no—
73C23×Dic3—24no—
74C23×Dic3—42no—
75C23×Dic3—42no—
76C23×Dic3D418yes—
77C23×Dic3C2312yes—
78C23×Dic3C2312yes—
79C23×Dic3C2312yes—
80C23×Dic3C2312yes—
81C2×C3×C22⋊C4—24no—
82C2×C3×C22⋊C4—22no—
83C2×C3×C22⋊C4—22no—
84C2×C3×C22⋊C4—22no—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—42no—
88C2×#217—24no—
89C2×#217—24no—
90C2×#217—24no—
91C2×#217—24no—
92C2×#217—24no—
93C2×#217—24no—
94C2×#217—24no—
95C2×#217—42no—
96C2×#217—42no—
97C2×C4⋊Dic3—22no—
98C2×C4⋊Dic3—22no—
99C2×C4⋊Dic3—22no—
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—42no—
102C2×Dic3⋊C4—24no—
103C2×Dic3⋊C4—24no—
104C2×Dic3⋊C4—24no—
105C2×Dic3⋊C4—24no—
106C2×Dic3⋊C4—42no—
107C2×Dic3⋊C4—42no—
108C3×#95—22no—
109C3×#95—22no—
110C3⋊#95—22no—
111C3⋊#95—24no—
112C3⋊#95—24no—
113C3⋊#95—24no—
114C3⋊#95—24no—
115C3⋊#95—24no—
116C3⋊#95—24no—
117C3⋊#95D414yescomplemented
118C23×D4C2×D311yescharacteristic
119C24×C4—32no—
120C24×C4C2×D311yescharacteristic
121C22×C4⋊C4—32no—
122C22×C4⋊C4—31no—
123C22×C4⋊C4—32no—
124C22×C4⋊C4—31no—
125C22×C22⋊C4—32no—
126C22×C22⋊C4—32no—
127C22×C22⋊C4—32no—
128C22×C22⋊C4C2×D311yescharacteristic
129C22×C22⋊C4C2×D311yescharacteristic
130C22×C22⋊C4C2×D311yescharacteristic
131#399—64no—
132#386—24no—
133#386—68no—
134#380—68no—
135#380—64no—
136C2×#95—31no—
137C2×#95—32no—
138C2×#95—31no—
139C2×#95—32no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95—32no—
143C2×#95—32no—
144C2×#95—64no—
145C2×#95C2×D311yescharacteristic
146C2×#95C2×D311yescharacteristic
147C24×C3—21no—
148C24×C3—22no—
149C24×C3—21no—
150C24×C3—21no—
151C24×C3—22no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—22no—
155C24×C3—21no—
156C24×C3—22no—
157C24×C3—21no—
158C24×C3—21no—
159C24×C3—22no—
160C24×C3—21no—
161C24×C3—22no—
162C24×C3—21no—
163C24×C3C2×D414yes—
164C24×C3C2×D412yes—
165C24×C3C2×Q812yes—
166C24×C3C2×Q812yes—
167C24×C3#4112yes—
168C24×C3#4114yes—
169C24×C3C2411yescharacteristic
170C2×C3×D4—216no—
171C2×C3×D4—28no—
172C2×C3×D4—48no—
173C2×C3×D4—44no—
174C2×C3×D4—44no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—28no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—28no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—44no—
198C22×C3×C4—48no—
199C22×C3×C4—48no—
200C22×C3×C4C2×D412yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×Q812yes—
204C22×C3×C4#4112yes—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—216no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—216no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—48no—
232C22×Dic3—48no—
233C22×Dic3—48no—
234C22×Dic3—48no—
235C22×Dic3—48no—
236C22×Dic3C2×D414yes—
237C22×Dic3C2×D414yes—
238C22×Dic3C2×D414yes—
239C22×Dic3#4114yes—
240C3×C22⋊C4—44no—
241C3×C22⋊C4—44no—
242C3×C22⋊C4—44no—
243#217—48no—
244#217—48no—
245#217—48no—
246C4⋊Dic3—44no—
247C4⋊Dic3—44no—
248Dic3⋊C4—48no—
249Dic3⋊C4—48no—
250C25C22×D311yescharacteristic
251C25C22×D311yescharacteristic
252C22×D4—22no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4Dic614yes—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—32no—
261C23×C4—32no—
262C23×C4—38no—
263C23×C4—32no—
264C23×C4—32no—
265C23×C4—42no—
266C23×C4—64no—
267C23×C4—64no—
268C23×C4—64no—
269C23×C4—64no—
270C23×C4—122no—
271C23×C4—122no—
272C23×C4#6714yes—
273C23×C4C22×D311yescharacteristic
274C23×C4C22×D311yescharacteristic
275C23×C4C22×D311yescharacteristic
276C23×C4C22×D311yescharacteristic
277C23×C4C22×D311yescharacteristic
278C2×C4⋊C4—64no—
279C2×C4⋊C4—64no—
280C2×C4⋊C4—64no—
281C2×C4⋊C4—64no—
282C2×C4⋊C4—62no—
283C2×C4⋊C4—62no—
284C2×C4⋊C4—62no—
285C2×C4⋊C4—62no—
286C2×C4⋊C4—122no—
287C2×C4⋊C4—122no—
288C2×C4⋊C4—122no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—64no—
297C2×C22⋊C4—64no—
298C2×C22⋊C4—64no—
299C2×C22⋊C4—64no—
300C2×C22⋊C4—64no—
301C2×C22⋊C4—64no—
302C2×C22⋊C4—64no—
303C2×C22⋊C4—122no—
304C2×C22⋊C4—122no—
305#95—22no—
306#95—22no—
307#95—34no—
308#95—64no—
309#95—64no—
310#95—64no—
311#95—64no—
312#95—64no—
313#95—62no—
314#95—64no—
315C23×C3—24no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—24no—
323C23×C3—22no—
324C23×C3—24no—
325C23×C3—22no—
326C23×C3—24no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—22no—
331C23×C3—24no—
332C23×C3—22no—
333C23×C3—24no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—24no—
337C23×C3—22no—
338C23×C3—42no—
339C23×C3—41no—
340C23×C3—42no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—42no—
349C23×C3—41no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—41no—
356C23×C3C22⋊Q818yes—
357C23×C3C22⋊Q814yes—
358C23×C3#12318yes—
359C23×C3#12314yes—
360C23×C3#12714yes—
361C23×C3C22×D411yescharacteristic
362C23×C3C22×D412yes—
363C23×C3C22×D411yescharacteristic
364C23×C3C22×Q811yescharacteristic
365C23×C3C2×#4111yescharacteristic
366C23×C3C2×#4111yescharacteristic
367C23×C3C2×#4112yes—
368C23×C3C2×#4112yes—
369C23×C3H(5,𝔽2)12yes—
370C23×C3H(5,𝔽2)11yescharacteristic
371C23×C32−1+411yescharacteristic
372C3×D4—416no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—416no—
383C2×C3×C4—42no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—42no—
398C2×C3×C4#12114yes—
399C2×Dic3—24no—
400C2×Dic3—24no—
401C2×Dic3—24no—
402C2×Dic3—24no—
403C2×Dic3—24no—
404C2×Dic3—24no—
405C2×Dic3—24no—
406C2×Dic3—24no—
407C2×Dic3—24no—
408C2×Dic3—432no—
409C2×Dic3—42no—
410C2×Dic3—42no—
411C2×Dic3—42no—
412C2×Dic3—42no—
413C2×Dic3—42no—
414C2×Dic3—42no—
415C2×Dic3—42no—
416C2×Dic3—42no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C2×Dic3#12118yes—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24C2×Dic612yes—
445C24C2×Dic612yes—
446C24#23512yes—
447C24D3×D414yes—
448C24#23714yes—
449C24C2×#6712yes—
450C24C23×D311yescharacteristic
451C2×D4—216no—
452C2×D4—28no—
453C2×D4—48no—
454C2×D4—44no—
455C2×D4—44no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—28no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—28no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—34no—
479C22×C4—34no—
480C22×C4—34no—
481C22×C4—34no—
482C22×C4—44no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4—616no—
486C22×C4—62no—
487C22×C4—62no—
488C22×C4—62no—
489C22×C4—62no—
490C22×C4—616no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—62no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—128no—
512C22×C4—128no—
513C22×C4—128no—
514C22×C4—128no—
515C22×C4—128no—
516C22×C4C2×Dic612yes—
517C22×C4D3×D412yes—
518C22×C4#23712yes—
519C22×C4C2×#6712yes—
520C22×C4C2×#6712yes—
521C4⋊C4—124no—
522C4⋊C4—128no—
523C4⋊C4—128no—
524C4⋊C4—124no—
525C22⋊C4—44no—
526C22⋊C4—44no—
527C22⋊C4—44no—
528C22⋊C4—128no—
529C22⋊C4—128no—
530C22⋊C4—128no—
531C22×C3—28no—
532C22×C3—24no—
533C22×C3—24no—
534C22×C3—24no—
535C22×C3—28no—
536C22×C3—24no—
537C22×C3—24no—
538C22×C3—28no—
539C22×C3—24no—
540C22×C3—28no—
541C22×C3—44no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—44no—
546C22×C3—81no—
547C22×C3—81no—
548C22×C3—82no—
549C22×C3—81no—
550C22×C3—81no—
551C22×C3—82no—
552C22×C3#39918yescomplemented
553C22×C3C2×#12111yescharacteristic
554C22×C3C2×#12112yes—
555C22×C3C2×C22⋊Q812yes—
556C22×C3C2×C22⋊Q811yescharacteristic
557C22×C3C2×#12312yes—
558C22×C3C2×#12311yescharacteristic
559C22×C3C2×#12711yescharacteristic
560C22×C3#53211yescharacteristic
561C22×C3#53212yes—
562C22×C3#53411yescharacteristic
563C22×C3#53412yes—
564C22×C3#53711yescharacteristic
565C22×C3#53712yes—
566C22×C3#54611yescharacteristic
567C22×C3#54612yes—
568C22×C3D4×Q811yescharacteristic
569C22×C3#55112yes—
570C22×C3#55112yes—
571C22×C3#55112yes—
572C22×C3#55212yes—
573C22×C3#55211yescharacteristic
574C22×C3#55412yes—
575C22×C3#55411yescharacteristic
576C3×C4—24no—
577C3×C4—42no—
578C3×C4—42no—
579C3×C4—81no—
580C3×C4—81no—
581Dic3—28no—
582Dic3—44no—
583Dic3—82no—
584Dic3—82no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—24no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—22no—
605C23—22no—
606C23—24no—
607C23—22no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—41no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23#87818yes—
627C23#88318yes—
628C23#92414yes—
629C23#93514yes—
630C23#94014yes—
631C23C22×Dic611yescharacteristic
632C23C2×#23511yescharacteristic
633C23C2×D3×D412yes—
634C23C2×D3×D411yescharacteristic
635C23C2×#23712yes—
636C23C2×#23711yescharacteristic
637C23#100412yes—
638C23D3×#4112yes—
639C23#100911yescharacteristic
640C23#101011yescharacteristic
641C23C22×#6711yescharacteristic
642D4—416no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—38no—
653C2×C4—416no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—64no—
670C2×C4—64no—
671C2×C4—64no—
672C2×C4—64no—
673C2×C4—64no—
674C2×C4—64no—
675C2×C4—64no—
676C2×C4—64no—
677C2×C4—64no—
678C2×C4—1232no—
679C2×C4—122no—
680C2×C4—122no—
681C2×C4—122no—
682C2×C4—122no—
683C2×C4—122no—
684C2×C4—122no—
685C2×C4—122no—
686C2×C4—122no—
687C2×C4—122no—
688C2×C4—122no—
689C2×C4—122no—
690C2×C4—122no—
691C2×C4—122no—
692C2×C4—122no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4—122no—
697C2×C4#93914yes—
698C2×C3—28no—
699C2×C3—82no—
700C2×C3C2×#39911yescharacteristic
701C2×C3#241212yes—
702C2×C3#241211yescharacteristic
703C2×C3#241711yescharacteristic
704C2×C3#241712yes—
705C2×C3#249811yescharacteristic
706C2×C3#249812yes—
707C2×C3#256412yes—
708C2×C3#256411yescharacteristic
709C2×C3#265611yescharacteristic
710C2×C3#285611yescharacteristic
711C22—28no—
712C22—24no—
713C22—28no—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—28no—
718C22—24no—
719C22—28no—
720C22—24no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—44no—
725C22—42no—
726C22—81no—
727C22—82no—
728C22—81no—
729C22—81no—
730C22—82no—
731C22—81no—
732C22#494918yescomplemented
733C22C2×#87812yes—
734C22C2×#88312yes—
735C22D4×Dic611yescharacteristic
736C22#553912yes—
737C22#554111yescharacteristic
738C22#554311yescharacteristic
739C22#555011yescharacteristic
740C22#555612yes—
741C22#558712yes—
742C22#559112yes—
743C22#559612yes—
744C22#559712yes—
745C22D3×#12112yes—
746C22#560512yes—
747C22#565012yes—
748C22#565812yes—
749C22C2×#92411yescharacteristic
750C22C2×#93511yescharacteristic
751C22C2×#93911yescharacteristic
752C22C2×#94011yescharacteristic
753C22#580411yescharacteristic
754C22#583211yescharacteristic
755C22#583311yescharacteristic
756C4—24no—
757C4—42no—
758C4—42no—
759C4—68no—
760C4—81no—
761C4—81no—
762C4—124no—
763C4—242no—
764C4—242no—
765C3#1483611yescharacteristic, complemented, Sylow
766C2—28no—
767C2—82no—
768C2#7469312yes—
769C2#7474112yes—
770C2#7476312yes—
771C2#7489012yes—
772C2C2×#494911yescharacteristic
773C2#8235311yescharacteristic
774C2#8238511yescharacteristic
775C2#8258411yescharacteristic
776C2#8268011yescharacteristic
777C2#8270011yescharacteristic
778C2#8285811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#386C2
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#14836
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#5212C2semidirect
4. C22×C3⋊#95C2semidirect
5. C2×#4949C2semidirect
6. C2×#4942C2semidirect
7. #71547C2semidirect
8. #71546C2semidirect
9. #69423C2semidirect
10. #69421C2semidirect
11. #69420C2semidirect
117. C3⋊#95D4semidirect
552. C22×C3#399semidirect
732. C22#4949semidirect
765. C3#14836semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×#52202
C2×#52122
C22×C3⋊#952
C2×#49492
C2×#49422
#715472
#715462
#694232
#694212
#694202
#148363