Finite Group Databasebeta

← #10830008

Subgroups — #10830008

Order 768.

1186 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5681C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3#82388C211yesmaximal, characteristic, complemented
4C2×C4×#213C211yesmaximal, characteristic, complemented
5#72055C211yesmaximal, characteristic, complemented
6#72048C211yesmaximal, characteristic, complemented
7#72044C211yesmaximal, characteristic
8#72037C211yesmaximal, characteristic, complemented
9#71725C211yesmaximal, characteristic, complemented
10#70480C211yesmaximal, characteristic, complemented
11#70472C211yesmaximal, characteristic, complemented
12#70279C211yesmaximal, characteristic, complemented
13#70235C211yesmaximal, characteristic, complemented
14#70211C211yesmaximal, characteristic, complemented
15#70167C211yesmaximal, characteristic, complemented
16#24192—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#947C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C2×#940C2211yescharacteristic
24C2×D4×Dic3C2211yescharacteristic
25C22×#213C2211yescharacteristic
26#5681—24no—
27#5681—24no—
28C2×#886—21no—
29C2×#885—21no—
30C2×#883—21no—
31C2×#67⋊C4—21no—
32C2×C4×D12C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C3×#463—24no—
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40#5221C2211yescharacteristic
41#5221C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45#5210—21no—
46#5210—21no—
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C4×#213—24no—
50#4972C2211yescharacteristic
51#4972C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#807C2211yescharacteristic
54#4949—21no—
55#4947—21no—
56#4936C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64C2×#559—31no—
65C2×#463D311yescharacteristic, complemented
66C2×C4×D8—31no—
67#2580—31no—
68#2042—31no—
69#2041—31no—
70#2012—31no—
71#2011—31no—
72#1984—31no—
73#1958—31no—
74#1880—31no—
75#1879—31no—
76#1863—31no—
77#1862—31no—
78#1804—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C22×#67—21no—
84C22×#67—21no—
85C23×Dic3—21no—
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×Dic6D411yescharacteristic
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—41no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C2×C3×D8—41no—
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×#124—22no—
98C3×#124D414yes—
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C42C2311yescharacteristic
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111#947—22no—
112#947—22no—
113Q8×Dic3—22no—
114Q8×Dic3—22no—
115#940—22no—
116#940—22no—
117D4×Dic3—22no—
118D4×Dic3—22no—
119C2×#213—22no—
120C2×#213—22no—
121C2×#213—22no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3D411yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4D411yescharacteristic
133C2×Dic3⋊C4D411yescharacteristic
134C2×C4×Dic3—21no—
135C2×C4×Dic3C2311yescharacteristic
136C2×C4×Dic3C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139#886—28no—
140#885—28no—
141#883—28no—
142#67⋊C4—28no—
143C4×D12—22no—
144C4×D12D414yes—
145C4×Dic6—22no—
146C4×Dic6—22no—
147C3×C4⋊C8—22no—
148C3×#103—22no—
149C3×#102—22no—
150#835—22no—
151#835—41no—
152#832—22no—
153#832—22no—
154#832—41no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—41no—
160#821—41no—
161#809—22no—
162#807—22no—
163C4×C3⋊C8—22no—
164C22×SD16C2×D311yescharacteristic
165C22×D8—31no—
166C22×D8C2×D311yescharacteristic
167#559—64no—
168#559—64no—
169C2×#127—31no—
170C2×#124—31no—
171C2×#124—61no—
172C2×#124C2×D311yescharacteristic
173C2×#123—61no—
174C2×#123—61no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—61no—
180C2×C4×D4C2×D311yescharacteristic
181#463—24no—
182C4×D8—64no—
183C2×#107—31no—
184C2×C4⋊C8C2×D311yescharacteristic
185C2×#103—31no—
186C2×#103—31no—
187C2×#103C2×D311yescharacteristic
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×C4×C8—31no—
196#399—61no—
197#393—61no—
198#390—31no—
199#390—31no—
200#389—31no—
201#389—31no—
202#385—61no—
203#385—61no—
204#382—31no—
205#340—31no—
206#340—31no—
207#336—31no—
208#336—31no—
209#336—31no—
210#336—31no—
211C24×C3—21no—
212C24×C3—21no—
213C23×D3—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8C2×D412yes—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4C2×D412yes—
231C2×C3×D4#4112yes—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—42no—
235C22×C3×C4—81no—
236C22×C3×C4—81no—
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C2×#67—24no—
241C2×#67—24no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—81no—
245C2×#67—81no—
246C22×Dic3—21no—
247C22×Dic3—24no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—81no—
251C22×Dic3—81no—
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12C2×D412yes—
262C2×C4×D3—24no—
263C2×C4×D3—81no—
264C2×C4×D3—81no—
265C2×Dic6—22no—
266C2×Dic6—22no—
267C2×Dic6—41no—
268C3×SD16—44no—
269C3×D8—44no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—42no—
281C3×C42C2×D412yes—
282C3×C42C2×D412yes—
283#217—24no—
284#217—42no—
285#217—42no—
286#217—81no—
287#217—81no—
288#213—28no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4—24no—
292C4⋊Dic3—24no—
293C4⋊Dic3—22no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3C2×D412yes—
300Dic3⋊C4—22no—
301Dic3⋊C4—22no—
302Dic3⋊C4—81no—
303Dic3⋊C4—81no—
304C4×Dic3—24no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C4×Dic3—21no—
308C4×Dic3—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8#4112yes—
315C22×Q8—31no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—31no—
318C22×D4—61no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C22×D4C22×D311yescharacteristic
322C23×C4—21no—
323C23×C4—61no—
324C23×C4—61no—
325C2×SD16—22no—
326C2×SD16—22no—
327C2×SD16—41no—
328C2×D8—22no—
329C2×D8—22no—
330C2×D8—41no—
331C2×D8—62no—
332C2×D8—62no—
333C2×D8—62no—
334C22×C8—31no—
335C22×C8—31no—
336C22×C8C22×D311yescharacteristic
337C22×C8C22×D311yescharacteristic
338#127—62no—
339#127—62no—
340#124—22no—
341#124—68no—
342#124—62no—
343#124—62no—
344#124#6714yes—
345#123—68no—
346#123—68no—
347C4×Q8—62no—
348C4×Q8—62no—
349C4×Q8—62no—
350C4×Q8—62no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—34no—
354C4×D4—68no—
355C4×D4—62no—
356C4×D4—62no—
357C4×D4—62no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4C22×D311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—61no—
382C2×C42C22×D311yescharacteristic
383#107—62no—
384C4⋊C8—22no—
385#103—22no—
386#103—62no—
387#103—121no—
388#102—22no—
389#102—62no—
390#102—62no—
391#102—62no—
392#102—121no—
393#102—121no—
394#102—121no—
395C4×C8—62no—
396#95—61no—
397#95—61no—
398#95—61no—
399#95—61no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3C22×D411yescharacteristic
415C22×D3—22no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C3×Q8—22no—
423C3×Q8—22no—
424C3×Q8—41no—
425C3×Q8—41no—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—41no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—84no—
445C2×C3×C4#12012yes—
446C2×C3×C4#12012yes—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C42−1+411yescharacteristic
453#67—48no—
454#67—84no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—22no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—84no—
476C2×Dic3#13512yes—
477D12—22no—
478D12—22no—
479D12—41no—
480D12—41no—
481C4×D3—84no—
482Dic6—44no—
483C3×C8—41no—
484C3×C8—41no—
485C3⋊C8—22no—
486C3⋊C8—41no—
487C24—21no—
488C24—21no—
489C24—61no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—62no—
496C2×Q8—62no—
497C2×Q8—121no—
498C2×Q8C2×#6712yes—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—32no—
510C2×D4—64no—
511C2×D4—64no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—122no—
518C2×D4—122no—
519C2×D4—241no—
520C2×D4—241no—
521C2×D4#23712yes—
522C2×D4C2×#6712yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—42no—
530C22×C4—61no—
531C22×C4—64no—
532C22×C4—64no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—241no—
538C22×C4—241no—
539C22×C4—241no—
540C22×C4—241no—
541C22×C4D3×D411yescharacteristic
542C22×C4D3×D411yescharacteristic
543C22×C4C23×D311yescharacteristic
544SD16—44no—
545D8—44no—
546D8—68no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—32no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—32no—
562C4⋊C4—64no—
563C4⋊C4—62no—
564C4⋊C4—62no—
565C4⋊C4—62no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—241no—
572C4⋊C4—241no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—42no—
576C22⋊C4—64no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—64no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—241no—
583C22⋊C4—241no—
584C42—64no—
585C42—61no—
586C42—61no—
587C42—61no—
588C42—61no—
589C42D3×D412yes—
590C42C2×#6712yes—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3C2×#12011yescharacteristic
606C22×C3#54811yescharacteristic
607C22×C3#55011yescharacteristic
608C22×C3C2×#13511yescharacteristic
609C22×C3#57511yescharacteristic
610C22×C3#57611yescharacteristic
611C22×C3#57611yescharacteristic
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—42no—
622C3×C4—81no—
623C3×C4#52511yescharacteristic
624C3×C4#53711yescharacteristic
625C3×C4#54611yescharacteristic
626C3×C4#54711yescharacteristic
627Dic3—22no—
628Dic3—41no—
629Dic3—42no—
630Dic3—41no—
631Dic3—41no—
632Dic3—81no—
633Dic3—81no—
634C23—22no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—62no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23C2×D3×D411yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—41no—
659Q8—41no—
660Q8—124no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—62no—
670D4—62no—
671D4—128no—
672D4—121no—
673D4—121no—
674D4—244no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—32no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—62no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—84no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—244no—
708C2×C4—244no—
709C2×C4#93712yes—
710C2×C4#93712yes—
711C2×C4C2×D3×D411yescharacteristic
712C2×C4C2×#23711yescharacteristic
713C2×C4#100411yescharacteristic
714C2×C4D3×#4111yescharacteristic
715C2×C4#101011yescharacteristic
716C2×C4C22×#6711yescharacteristic
717C8—41no—
718C8—41no—
719C8—62no—
720C8—121no—
721C2×C3—82no—
722C2×C3—82no—
723C2×C3#240711yescharacteristic
724C2×C3#300211yescharacteristic
725C2×C3#300811yescharacteristic
726C2×C3#336111yescharacteristic
727C2×C3#337011yescharacteristic
728C2×C3#339611yescharacteristic
729C2×C3#340311yescharacteristic
730D3—82no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—122no—
746C22—122no—
747C22—122no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22—241no—
752C22#559811yescharacteristic
753C22#559911yescharacteristic
754C22D3×#13511yescharacteristic
755C22#576811yescharacteristic
756C22#577411yescharacteristic
757C22#577411yescharacteristic
758C22C2×#93711yescharacteristic
759C4—22no—
760C4—22no—
761C4—42no—
762C4—62no—
763C4—81no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4—122no—
768C4—241no—
769C4—241no—
770C4#560611yescharacteristic
771C4#560811yescharacteristic
772C4#580611yescharacteristic
773C4#582411yescharacteristic
774C3#2419211yescharacteristic, complemented, Sylow
775C2—82no—
776C2—82no—
777C2—242no—
778C2#8051711yescharacteristic
779C2#8051911yescharacteristic
780C2#8052511yescharacteristic
781C2#8053011yescharacteristic
782C2#8270111yescharacteristic
783C2#8391111yescharacteristic
784C2#8394711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#463C2
socleC23×C3C22×D4
prime radical#72044C2
hypercenterC2×#463D3
hypocenterC3#24192
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#5681C2semidirect
2. C2×C3×#463C2semidirect
3. #82388C2semidirect
4. C2×C4×#213C2semidirect
5. #72055C2semidirect
6. #72048C2semidirect
8. #72037C2semidirect
9. #71725C2semidirect
10. #70480C2semidirect
11. #70472C2semidirect
12. #70279C2semidirect
13. #70235C2semidirect
14. #70211C2semidirect
15. #70167C2semidirect
65. C2×#463D3semidirect
774. C3#24192semidirect

Maximal subgroups

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

subgroupindex
C2×#56812
C2×C3×#4632
#823882
C2×C4×#2132
#720552
#720482
#720442
#720372
#717252
#704802
#704722
#702792
#702352
#702112
#701672
#241923