Finite Group Databasebeta

← #11792806

Subgroups — #11792806

Order 1152.

1381 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#882C211yesmaximal, characteristic, complemented
2#10595519C211yesmaximal, characteristic, complemented
3C2×#63977C211yesmaximal, characteristic, complemented
4C2×#63633C211yesmaximal, characteristic, complemented
5#10591706C211yesmaximal, characteristic, complemented
6C2×#63580C211yesmaximal, characteristic, complemented
7C3×#4527C211yesmaximal, characteristic, complemented
8#71671—31nomaximal
9#68965—31nomaximal
10C24×C3×D3C2211yescharacteristic
11C22×#638C2211yescharacteristic
12C22×C3×#67C2211yescharacteristic
13C22×C3×D12—21no—
14C22×#626—21no—
15C2×C32×C22⋊C4C2211yescharacteristic
16C2×#3757C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C2×C3×#217C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4—21no—
20C3×#882—22no—
21C3×#882—22no—
22#63981—21no—
23#63978—22no—
24#63977—22no—
25#63977—22no—
26#63977—21no—
27#63966—21no—
28#63962—21no—
29C2×(C2×D3)⋊Dic3—21no—
30C2×(C2×D3)⋊Dic3—22no—
31#63633—22no—
32#63580—22no—
33C2×C3×#120—31no—
34C2×#953—31no—
35#5804—31no—
36#5493—31no—
37C2×#882—31no—
38C2×#882D311yescharacteristic, complemented
39#5247—31no—
40C2×#834—31no—
41#4955—31no—
42C2×#806—31no—
43C2×#806—31no—
44C2×#806—31no—
45C2×#806—61no—
46C3×#342—31no—
47#4527D311yescharacteristic, complemented
48C24×C32C2311yescharacteristic
49C23×C3⋊D3D411yescharacteristic, complemented
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C23×C3×D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3—21no—
55C23×C3×D3—21no—
56C23×C3×D3—44no—
57C23×C3×D3D412yescomplemented
58C23×C3×D3D411yescharacteristic, complemented
59C22×C32×C4—21no—
60C2×#638—21no—
61C2×#638—21no—
62C2×#638—21no—
63C2×#638—21no—
64C2×#638—21no—
65C2×#638—21no—
66C22×C3⋊Dic3—21no—
67C22×C3⋊Dic3D411yescharacteristic, complemented
68C2×C3×#67—21no—
69C2×C3×#67—21no—
70C2×C3×#67—21no—
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C22×C3×Dic3—21no—
75C22×C3×Dic3D411yescharacteristic, complemented
76C22×C3×Dic3D412yescomplemented
77C2×C3×D12—24no—
78C2×C3×D12—44no—
79C2×#626—24no—
80C2×#626—22no—
81C2×#626—44no—
82C32×C22⋊C4—21no—
83C32×C22⋊C4D412yescomplemented
84#3757—21no—
85#3757—21no—
86C3×#217—21no—
87C3×#217—21no—
88C3×#217—21no—
89C3×#217D412yescomplemented
90C3×(C2×D3)⋊C4—24no—
91Dic3⋊Dic3—22no—
92#3722—22no—
93(C2×D3)⋊Dic3—24no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—44no—
96#2021—91noSylow
97C25×C3—31no—
98C24×D3C2×D311yescharacteristic
99C22×C3×D4—31no—
100C22×C3×D4—61no—
101C22×#67—31no—
102C22×#67—31no—
103C22×#67—61no—
104C22×#67—61no—
105C22×#67C2×D311yescharacteristic
106C22×D12—21no—
107C22×D12—61no—
108C3×#120—62no—
109C3×#120—62no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—31no—
112C2×C3×C22⋊C4—31no—
113C2×C3×C22⋊C4—61no—
114C2×C3×C22⋊C4C2×D311yescharacteristic
115C2×C3×C22⋊C4C2×D311yescharacteristic
116#953—61no—
117#953—62no—
118#953—62no—
119C2×#217—31no—
120C2×#217—31no—
121C2×#217—61no—
122C2×#217—61no—
123C2×#217—62no—
124C2×#217C2×D311yescharacteristic
125C2×#217C2×D311yescharacteristic
126#939—62no—
127#937—61no—
128#935—61no—
129#930—62no—
130#929—61no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—61no—
133C2×(C2×D3)⋊C4—62no—
134#886—61no—
135#886—61no—
136#882—22no—
137#882—22no—
138#882—62no—
139#882—61no—
140#882—62no—
141#882—61no—
142#834—62no—
143#806—64no—
144#806—62no—
145#806—62no—
146#806—62no—
147C23×C32—42no—
148C23×C32C2×D411yescharacteristic
149C23×C32C2×D411yescharacteristic
150C23×C32C2×D411yescharacteristic
151C23×C32C2×D411yescharacteristic
152C23×C32C2×D411yescharacteristic
153C23×C32C2×D411yescharacteristic
154C23×C32#4111yescharacteristic
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3—42no—
159C22×C3×D3—24no—
160C22×C3×D3—24no—
161C22×C3×D3—24no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3—21no—
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—44no—
169C22×C3×D3—44no—
170C22×C3×D3—44no—
171C22×C3×D3—44no—
172C22×C3×D3—42no—
173C22×C3×D3—42no—
174C22×C3×D3—42no—
175C22×C3×D3—41no—
176C22×C3×D3—41no—
177C22×C3×D3—41no—
178C22×C3×D3—41no—
179C22×C3×D3—42no—
180C2×C32×C4—22no—
181C2×C32×C4—42no—
182#638—41no—
183#638—41no—
184#638—41no—
185#638—41no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—41no—
190C2×C3⋊Dic3—42no—
191C3×#67—41no—
192C3×#67—41no—
193C3×#67—41no—
194C3×#67—41no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—42no—
201C2×C3×Dic3—42no—
202C3×D12—48no—
203#626—48no—
204#626—82no—
205#534—91no—
206C2×#120—31no—
207C2×#120—91no—
208C2×#99—91no—
209C2×#99—91no—
210#379—91no—
211#342—31no—
212C24×C3—21no—
213C24×C3—32no—
214C24×C3—31no—
215C24×C3—61no—
216C24×C3—61no—
217C24×C3—61no—
218C24×C3—61no—
219C24×C3—61no—
220C24×C3—61no—
221C24×C3—124no—
222C24×C3C22×D311yescharacteristic
223C24×C3C22×D311yescharacteristic
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—31no—
231C23×D3—31no—
232C23×D3—44no—
233C23×D3—61no—
234C23×D3#6712yescomplemented
235C23×D3#6711yescharacteristic, complemented
236C2×C3×D4—64no—
237C2×C3×D4—61no—
238C2×C3×D4—61no—
239C2×C3×D4—61no—
240C2×C3×D4—61no—
241C2×C3×D4—61no—
242C2×C3×D4—61no—
243C2×C3×D4—124no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—31no—
247C22×C3×C4—32no—
248C22×C3×C4—41no—
249C22×C3×C4—61no—
250C2×#67—21no—
251C2×#67—21no—
252C2×#67—21no—
253C2×#67—21no—
254C2×#67—21no—
255C2×#67—21no—
256C2×#67—64no—
257C2×#67—62no—
258C2×#67—62no—
259C2×#67—62no—
260C2×#67—61no—
261C2×#67—61no—
262C2×#67—61no—
263C2×#67—61no—
264C2×#67—61no—
265C2×#67—61no—
266C2×#67—61no—
267C2×#67—61no—
268C2×#67—61no—
269C2×#67—61no—
270C2×#67—61no—
271C2×#67—61no—
272C2×#67—121no—
273C2×#67—121no—
274C2×#67—121no—
275C2×#67—121no—
276C2×#67—124no—
277C22×Dic3—21no—
278C22×Dic3—31no—
279C22×Dic3—31no—
280C22×Dic3—61no—
281C22×Dic3—61no—
282C22×Dic3—61no—
283C22×Dic3—121no—
284C22×Dic3D1212yescomplemented
285C22×Dic3#6711yescharacteristic, complemented
286C2×D12—24no—
287C2×D12—44no—
288C2×D12—64no—
289C2×D12—62no—
290C2×D12—124no—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—22no—
294C3×C22⋊C4—32no—
295C3×C22⋊C4—41no—
296C3×C22⋊C4—64no—
297C3×C22⋊C4—61no—
298C3×C22⋊C4—61no—
299C3×C22⋊C4—61no—
300C3×C22⋊C4D1212yescomplemented
301C3×C22⋊C4#6712yescomplemented
302#217—21no—
303#217—21no—
304#217—21no—
305#217—62no—
306#217—64no—
307#217—62no—
308#217—61no—
309#217—61no—
310#217—61no—
311#217—61no—
312#217—121no—
313#217—124no—
314#217D1212yescomplemented
315(C2×D3)⋊C4—24no—
316(C2×D3)⋊C4—62no—
317(C2×D3)⋊C4—62no—
318(C2×D3)⋊C4—64no—
319(C2×D3)⋊C4—62no—
320(C2×D3)⋊C4—124no—
321C4⋊Dic3—62no—
322Dic3⋊C4—62no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—41no—
327C22×C32—41no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32#12011yescharacteristic
331C22×C32#12011yescharacteristic
332C22×C32#12011yescharacteristic
333C22×C32#12111yescharacteristic
334C22×C32#12111yescharacteristic
335C22×C32#12111yescharacteristic
336C22×C32#12711yescharacteristic
337C2×C3⋊D3—41no—
338C2×C3⋊D3—42no—
339C2×C3⋊D3—42no—
340C2×C3⋊D3—81no—
341C2×C3×D3—24no—
342C2×C3×D3—24no—
343C2×C3×D3—24no—
344C2×C3×D3—42no—
345C2×C3×D3—44no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348C2×C3×D3—44no—
349C2×C3×D3—44no—
350C2×C3×D3—42no—
351C2×C3×D3—44no—
352C2×C3×D3—42no—
353C2×C3×D3—41no—
354C2×C3×D3—42no—
355C2×C3×D3—81no—
356C32×C4—42no—
357C3⋊Dic3—41no—
358C3⋊Dic3—81no—
359C3×Dic3—42no—
360C3×Dic3—41no—
361C3×Dic3—42no—
362C25—31no—
363C22×D4—31no—
364C22×D4—61no—
365C22×D4—91no—
366C22×D4—181no—
367#123—181no—
368#123—181no—
369#121—182no—
370#120—62no—
371#120—62no—
372#120—182no—
373#120—181no—
374#120—182no—
375#120—181no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—91no—
380C2×C22⋊C4—181no—
381C2×C22⋊C4—182no—
382C2×C22⋊C4D3211yescharacteristic
383#99—182no—
384#99—182no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—64no—
395C23×C3—64no—
396C23×C3—64no—
397C23×C3—62no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3—61no—
401C23×C3—61no—
402C23×C3—61no—
403C23×C3—82no—
404C23×C3—122no—
405C23×C3—122no—
406C23×C3—122no—
407C23×C3—122no—
408C23×C3—124no—
409C23×C3—124no—
410C23×C3—124no—
411C23×C3—124no—
412C23×C3—121no—
413C23×C3—121no—
414C23×C3—121no—
415C23×C3—121no—
416C23×C3C2×D1211yescharacteristic
417C23×C3C2×D1211yescharacteristic
418C23×C3C2×D1211yescharacteristic
419C23×C3D3×D411yescharacteristic
420C23×C3D3×D411yescharacteristic
421C23×C3D3×D411yescharacteristic
422C23×C3D3×D411yescharacteristic
423C23×C3D3×D411yescharacteristic
424C23×C3D3×D411yescharacteristic
425C23×C3#23711yescharacteristic
426C23×C3#23911yescharacteristic
427C23×C3C2×#6711yescharacteristic
428C23×C3C2×#6711yescharacteristic
429C23×C3C2×#6711yescharacteristic
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—24no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—44no—
440C22×D3—44no—
441C22×D3—44no—
442C22×D3—44no—
443C22×D3—42no—
444C22×D3—42no—
445C22×D3—42no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—42no—
451C22×D3—61no—
452C22×D3—61no—
453C22×D3—61no—
454C22×D3—61no—
455C22×D3—62no—
456C22×D3—61no—
457C22×D3—61no—
458C22×D3—121no—
459C22×D3—121no—
460C22×D3—122no—
461C22×D3—122no—
462C22×D3—242no—
463C3×D4—128no—
464C3×D4—121no—
465C3×D4—121no—
466C3×D4—121no—
467C3×D4—121no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—82no—
479C2×C3×C4—122no—
480C2×C3×C4—122no—
481#67—41no—
482#67—41no—
483#67—41no—
484#67—41no—
485#67—128no—
486#67—122no—
487#67—122no—
488#67—122no—
489#67—122no—
490#67—121no—
491#67—121no—
492#67—121no—
493#67—121no—
494#67—121no—
495#67—121no—
496#67—121no—
497#67—121no—
498#67—242no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—42no—
505C2×Dic3—42no—
506C2×Dic3—62no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—121no—
514C2×Dic3—121no—
515C2×Dic3—122no—
516C2×Dic3—122no—
517C2×Dic3—122no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—242no—
521D12—48no—
522D12—128no—
523D12—242no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32#39211yescharacteristic
531C2×C32B(4,𝔽2)12yes—
532C3⋊D3—81no—
533C3×D3—44no—
534C3×D3—81no—
535C24—32no—
536C24—31no—
537C24—61no—
538C24—61no—
539C24—61no—
540C24—61no—
541C24—61no—
542C24—61no—
543C24—91no—
544C24—124no—
545C24C2×D3211yescharacteristic
546C2×D4—64no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—124no—
554C2×D4—184no—
555C2×D4—182no—
556C2×D4—181no—
557C2×D4—181no—
558C2×D4—181no—
559C2×D4—181no—
560C2×D4—181no—
561C2×D4—181no—
562C2×D4—364no—
563C22×C4—21no—
564C22×C4—31no—
565C22×C4—32no—
566C22×C4—61no—
567C22×C4—91no—
568C22×C4—181no—
569C4⋊C4—182no—
570C22⋊C4—21no—
571C22⋊C4—32no—
572C22⋊C4—64no—
573C22⋊C4—61no—
574C22⋊C4—61no—
575C22⋊C4—61no—
576C22⋊C4—182no—
577C22⋊C4—184no—
578C22⋊C4—182no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C22⋊C4—364no—
582C22⋊C4#62612yescomplemented
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—64no—
608C22×C3—64no—
609C22×C3—64no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3—122no—
615C22×C3—124no—
616C22×C3—122no—
617C22×C3—124no—
618C22×C3—122no—
619C22×C3—124no—
620C22×C3—122no—
621C22×C3—122no—
622C22×C3—124no—
623C22×C3—121no—
624C22×C3—122no—
625C22×C3—241no—
626C22×C3#87411yescharacteristic
627C22×C3#88211yescharacteristic
628C22×C3#88211yescharacteristic
629C22×C3#88211yescharacteristic
630C22×C3#89511yescharacteristic
631C22×C3#89511yescharacteristic
632C22×C3#89511yescharacteristic
633C22×C3#93711yescharacteristic
634C22×C3#93711yescharacteristic
635C22×C3#93811yescharacteristic
636C22×C3#93911yescharacteristic
637C22×C3#93911yescharacteristic
638C22×C3#94011yescharacteristic
639C22×C3#95311yescharacteristic
640C2×D3—24no—
641C2×D3—24no—
642C2×D3—24no—
643C2×D3—44no—
644C2×D3—42no—
645C2×D3—42no—
646C2×D3—42no—
647C2×D3—44no—
648C2×D3—44no—
649C2×D3—42no—
650C2×D3—44no—
651C2×D3—42no—
652C2×D3—41no—
653C2×D3—42no—
654C2×D3—81no—
655C2×D3—122no—
656C2×D3—122no—
657C2×D3—122no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—122no—
661C2×D3—122no—
662C2×D3—242no—
663C2×D3—242no—
664C2×D3—241no—
665C2×D3—241no—
666C2×D3—242no—
667C3×C4—42no—
668C3×C4—42no—
669C3×C4—82no—
670C3×C4—122no—
671C3×C4—121no—
672C3×C4—122no—
673Dic3—42no—
674Dic3—41no—
675Dic3—42no—
676Dic3—122no—
677Dic3—121no—
678Dic3—121no—
679Dic3—241no—
680Dic3—241no—
681Dic3—242no—
682C32#202111yescharacteristic, complemented, Sylow
683C23—42no—
684C23—64no—
685C23—64no—
686C23—64no—
687C23—62no—
688C23—62no—
689C23—62no—
690C23—61no—
691C23—61no—
692C23—61no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—124no—
698C23—124no—
699C23—124no—
700C23—124no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23—121no—
705C23—181no—
706C23—181no—
707C23—181no—
708C23—362no—
709C23#379611yescharacteristic
710C23D3×D1211yescharacteristic
711C23D3×D1211yescharacteristic
712C23#380211yescharacteristic
713C23C2×#62611yescharacteristic
714C23D3×#6711yescharacteristic
715C23D3×#6711yescharacteristic
716D4—128no—
717D4—121no—
718D4—121no—
719D4—121no—
720D4—121no—
721D4—368no—
722D4—361no—
723D4—361no—
724D4—361no—
725D4—361no—
726D4—722no—
727C2×C4—22no—
728C2×C4—42no—
729C2×C4—61no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—362no—
740C2×C4—361no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—22no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—124no—
762C2×C3—241no—
763C2×C3#467111yescharacteristic
764C2×C3#474112yes—
765C2×C3#503212yes—
766C2×C3#522311yescharacteristic
767D3—44no—
768D3—81no—
769D3—242no—
770D3—241no—
771D3—241no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—64no—
780C22—64no—
781C22—64no—
782C22—122no—
783C22—122no—
784C22—124no—
785C22—122no—
786C22—124no—
787C22—124no—
788C22—122no—
789C22—122no—
790C22—124no—
791C22—121no—
792C22—122no—
793C22—241no—
794C22—362no—
795C22—361no—
796C22—362no—
797C22—721no—
798C22#6388611yescharacteristic
799C22#6388611yescharacteristic
800C22#6391111yescharacteristic
801C22#6391611yescharacteristic
802C22#6392211yescharacteristic
803C22#6392211yescharacteristic
804C22#6397711yescharacteristic
805C4—42no—
806C4—122no—
807C4—121no—
808C4—122no—
809C4—361no—
810C4—721no—
811C3—21no—
812C3#6896511yescharacteristic, complemented
813C3#7167111yescharacteristic, complemented
814C2—21no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—124no—
821C2—241no—
822C2—721no—
823C2#1059040712yes—
824C2#1059139111yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC24×C32C23
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
hypercenterC2×C22⋊C4D32
hypocenterC32#2021
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#882C2semidirect
2. #10595519C2semidirect
3. C2×#63977C2semidirect
4. C2×#63633C2semidirect
5. #10591706C2semidirect
6. C2×#63580C2semidirect
7. C3×#4527C2semidirect
38. C2×#882D3semidirect
47. #4527D3semidirect
49. C23×C3⋊D3D4semidirect
57. C23×C3×D3D4semidirect
58. C23×C3×D3D4semidirect
67. C22×C3⋊Dic3D4semidirect
75. C22×C3×Dic3D4semidirect
76. C22×C3×Dic3D4semidirect
83. C32×C22⋊C4D4semidirect
89. C3×#217D4semidirect
234. C23×D3#67semidirect
235. C23×D3#67semidirect
284. C22×Dic3D12semidirect
285. C22×Dic3#67semidirect
300. C3×C22⋊C4D12semidirect
301. C3×C22⋊C4#67semidirect
314. #217D12semidirect
582. C22⋊C4#626semidirect
682. C32#2021semidirect
812. C3#68965semidirect
813. C3#71671semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8822
#105955192
C2×#639772
C2×#636332
#105917062
C2×#635802
C3×#45272
#716713
#689653