Finite Group Databasebeta

← #10702098

Subgroups — #10702098

Order 768.

1374 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5822C211yesmaximal, characteristic
2C2×C3×#421C211yesmaximal, characteristic, complemented
3#84086C211yesmaximal, characteristic, complemented
4C2×#5139C211yesmaximal, characteristic, complemented
5#82228C211yesmaximal, characteristic, complemented
6#71979C211yesmaximal, characteristic, complemented
7C2×#4531C211yesmaximal, characteristic, complemented
8#11041—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×#235C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C2×C3×#117C2211yescharacteristic
13C2×#951—21no—
14#5822—22no—
15#5822—22no—
16#5822—22no—
17#5822C414yescomplemented
18C2×#950—22no—
19C2×#949—21no—
20C2×#942—21no—
21C2×#932—21no—
22C2×#926C2211yescharacteristic
23C22×C4×Dic3C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C3×#421—22no—
26C3×#421—22no—
27C2×C3×#104—22no—
28#5229—21no—
29#5221—21no—
30#5220—22no—
31C4×#217—22no—
32#5139—22no—
33#5139—22no—
34C2×#825—22no—
35#4988—21no—
36#4973—21no—
37#4958—22no—
38C4×(C2×D3)⋊C4—22no—
39#4550—22no—
40#4531—22no—
41C2×#575—31no—
42C2×#421—31no—
43C2×#421D311yescharacteristic, complemented
44#2297—31no—
45#2297—31no—
46C2×H(3,ℤ/4)—31no—
47#1728—31no—
48C2×C3×#41—21no—
49C2×C3×#41—21no—
50C2×C3×#41—21no—
51C2×C3×#41—21no—
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41—21no—
57C2×C3×#41—21no—
58C2×C3×#41C2×C412yes—
59C2×C3×#41D412yes—
60C22×C3×Q8D411yescharacteristic
61C22×C3×D4—21no—
62C22×C3×D4D411yescharacteristic
63C23×C3×C4—21no—
64C23×C3×C4C2311yescharacteristic
65C22×#67—21no—
66C23×Dic3D412yes—
67C2×#235—21no—
68C2×#235—21no—
69C2×#235—21no—
70C2×#235—21no—
71C2×#235—21no—
72C2×#235—21no—
73C2×#235—21no—
74C2×#235—21no—
75C2×#235—21no—
76C2×#235—21no—
77C2×#235C2×C412yes—
78C2×#235D412yes—
79C22×D12D411yescharacteristic
80C22×C4×D3—21no—
81C22×Dic6D411yescharacteristic
82C2×C3×M16—21no—
83C2×C3×M16—21no—
84C2×C3×M16—21no—
85C2×C3×M16—21no—
86C2×C3×M16—21no—
87C2×C3×M16D412yes—
88C22×C3×C8—21no—
89C3×#117—21no—
90C3×#117—21no—
91C3×#117—21no—
92C3×#117—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C22⋊C4—21no—
95C2×C3×C42D412yes—
96C2×#217—24no—
97C2×#217—21no—
98#951—24no—
99#951—24no—
100#950—28no—
101#950—28no—
102#949—24no—
103#949—24no—
104C2×#216—22no—
105#942—24no—
106#942—24no—
107C2×#215—22no—
108C2×#214—22no—
109#932—24no—
110#932—24no—
111C2×#213—22no—
112C2×(C2×D3)⋊C4—24no—
113#926—21no—
114#926—21no—
115#926—21no—
116#926—21no—
117C2×C4⋊Dic3—21no—
118C2×C4×Dic3—21no—
119C2×C4×Dic3—21no—
120C2×C4×Dic3—21no—
121C2×C4×Dic3—21no—
122C2×C4×Dic3—21no—
123C2×C4×Dic3—21no—
124C2×C4×Dic3D412yes—
125C2×#208—21no—
126C2×#208—21no—
127C2×#208—21no—
128C2×#208—21no—
129C2×#208C2×C412yes—
130C2×#208D412yes—
131C22×C3⋊C8D412yes—
132C3×#104—28no—
133C3⋊#95—24no—
134C3⋊#95—24no—
135#825—28no—
136C22×#41—31no—
137C22×#41C2×D311yescharacteristic
138#575—34no—
139#575—62no—
140#575—62no—
141#575—62no—
142C2×#137—61no—
143C2×#137—61no—
144C2×AGL(1,ℤ/8)—61no—
145C2×AGL(1,ℤ/8)—61no—
146C2×#135—62no—
147C22×M16—31no—
148C22×M16C2×D311yescharacteristic
149C2×#117—31no—
150C2×#117C2×D311yescharacteristic
151C22×C42—31no—
152#421—22no—
153#421—22no—
154#421—62no—
155#421—62no—
156C2×#104—22no—
157C2×#104—62no—
158#391—61no—
159#391—61no—
160#390—61no—
161#390—61no—
162#386—62no—
163#386—62no—
164C4×C22⋊C4—62no—
165C4×C22⋊C4—62no—
166H(3,ℤ/4)—62no—
167#336—62no—
168C24×C3—21no—
169C24×C3C2×D411yescharacteristic
170C23×D3—21no—
171C3×#41—22no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—22no—
175C3×#41—22no—
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—22no—
179C3×#41—41no—
180C3×#41—41no—
181C3×#41—41no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—41no—
185C3×#41—41no—
186C3×#41—41no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8C22⋊C412yescomplemented
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4—41no—
204C2×C3×D4C22⋊C412yescomplemented
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—41no—
210C22×C3×C4—41no—
211C22×C3×C4—41no—
212C22×C3×C4—41no—
213C22×C3×C4C22×C411yescharacteristic
214C22×C3×C4C2×D411yescharacteristic
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4#4111yescharacteristic
224C22×C3×C4#4111yescharacteristic
225C22×C3×C4#4111yescharacteristic
226C22×C3×C4#4111yescharacteristic
227C2×#67—22no—
228C2×#67—22no—
229C2×#67—41no—
230C2×#67—41no—
231C2×#67—41no—
232C2×#67—41no—
233C22×Dic3—21no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—44no—
239#235—22no—
240#235—22no—
241#235—22no—
242#235—22no—
243#235—22no—
244#235—22no—
245#235—22no—
246#235—22no—
247#235—41no—
248#235—41no—
249#235—41no—
250#235—41no—
251#235—41no—
252#235—41no—
253#235—41no—
254#235—41no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12C22⋊C412yescomplemented
261C2×C4×D3—22no—
262C2×C4×D3—22no—
263C2×C4×D3—41no—
264C2×C4×D3—41no—
265C2×C4×D3—41no—
266C2×C4×D3—41no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6C22⋊C412yescomplemented
273C3×M16—22no—
274C3×M16—22no—
275C3×M16—41no—
276C3×M16—41no—
277C2×C3×C8—22no—
278C2×C3×C8—41no—
279C2×C3×C8—41no—
280C3×C4⋊C4—41no—
281C3×C4⋊C4—41no—
282C3×C22⋊C4—41no—
283C3×C22⋊C4—41no—
284C3×C42—22no—
285C3×C42—22no—
286#217—48no—
287#217—41no—
288#217—41no—
289#216—28no—
290#215—28no—
291#214—28no—
292#213—28no—
293(C2×D3)⋊C4—48no—
294C4⋊Dic3—41no—
295C4⋊Dic3—41no—
296C4×Dic3—22no—
297C4×Dic3—22no—
298C4×Dic3—41no—
299C4×Dic3—41no—
300C4×Dic3—41no—
301C4×Dic3—41no—
302#208—22no—
303#208—22no—
304#208—22no—
305#208—22no—
306C2×C3⋊C8—22no—
307C2×C3⋊C8—22no—
308C2×C3⋊C8C22⋊C414yescomplemented
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—21no—
312C2×#41—21no—
313C2×#41—21no—
314C2×#41—21no—
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—21no—
318C2×#41—21no—
319C2×#41—32no—
320C2×#41—32no—
321C2×#41—61no—
322C2×#41—61no—
323C2×#41—61no—
324C2×#41—61no—
325C2×#41—61no—
326C2×#41—61no—
327C2×#41—61no—
328C2×#41—61no—
329C2×#41—61no—
330C2×#41—61no—
331C2×#41C4×D312yes—
332C2×#41#6712yes—
333C22×Q8—31no—
334C22×Q8D1211yescharacteristic
335C22×D4—21no—
336C22×D4—31no—
337C22×D4—61no—
338C22×D4D1211yescharacteristic
339C23×C4—21no—
340C23×C4—32no—
341C23×C4—61no—
342C23×C4C22×D311yescharacteristic
343#137—64no—
344#137—64no—
345#137—64no—
346#137—64no—
347AGL(1,ℤ/8)—64no—
348AGL(1,ℤ/8)—64no—
349AGL(1,ℤ/8)—64no—
350AGL(1,ℤ/8)—64no—
351#135—68no—
352#135—68no—
353C2×Q16—62no—
354C2×SD16—62no—
355C2×SD16—62no—
356C2×D8—62no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—32no—
363C2×M16—32no—
364C2×M16—61no—
365C2×M16—61no—
366C2×M16—61no—
367C2×M16—61no—
368C2×M16#6712yes—
369C22×C8—21no—
370C22×C8—32no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—61no—
376#117—61no—
377#117—61no—
378#117—61no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—61no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—64no—
383C2×C22⋊C4—64no—
384C2×C22⋊C4—61no—
385C2×C42—32no—
386C2×C42—61no—
387C2×C42—61no—
388C2×C42—61no—
389C2×C42—61no—
390C2×C42—61no—
391C2×C42—61no—
392C2×C42#6712yes—
393#104—28no—
394#104—68no—
395#95—64no—
396#95—64no—
397C23×C3—22no—
398C23×C3—42no—
399C23×C3—44no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3C4×D411yescharacteristic
403C23×C3#12011yescharacteristic
404C23×C3#12011yescharacteristic
405C23×C3#12111yescharacteristic
406C23×C3#12111yescharacteristic
407C23×C3#12111yescharacteristic
408C23×C3#12711yescharacteristic
409C22×D3—22no—
410C22×D3—44no—
411C22×D3—41no—
412C22×D3—41no—
413C3×Q8—22no—
414C3×Q8—22no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×D4—22no—
418C3×D4—22no—
419C3×D4—42no—
420C3×D4—42no—
421C3×D4—42no—
422C3×D4—42no—
423C3×D4—41no—
424C3×D4—41no—
425C2×C3×C4—22no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—44no—
433C2×C3×C4—42no—
434C2×C3×C4C2×C22⋊C411yescharacteristic
435C2×C3×C4C2×C22⋊C411yescharacteristic
436C2×C3×C4C2×C22⋊C411yescharacteristic
437C2×C3×C4C4×D411yescharacteristic
438C2×C3×C4C4×D411yescharacteristic
439C2×C3×C4C4×D411yescharacteristic
440C2×C3×C4#12011yescharacteristic
441C2×C3×C4#12011yescharacteristic
442C2×C3×C4#12011yescharacteristic
443C2×C3×C4#12011yescharacteristic
444C2×C3×C4#12011yescharacteristic
445C2×C3×C4#12011yescharacteristic
446C2×C3×C4#12111yescharacteristic
447C2×C3×C4#12111yescharacteristic
448C2×C3×C4#12111yescharacteristic
449C2×C3×C4#12111yescharacteristic
450C2×C3×C4#12111yescharacteristic
451C2×C3×C4#12111yescharacteristic
452C2×C3×C4#12111yescharacteristic
453C2×C3×C4#12111yescharacteristic
454C2×C3×C4#12111yescharacteristic
455C2×C3×C4#12311yescharacteristic
456C2×C3×C4#12311yescharacteristic
457C2×C3×C4#12311yescharacteristic
458C2×C3×C4#12311yescharacteristic
459C2×C3×C4#12411yescharacteristic
460C2×C3×C4#12411yescharacteristic
461C2×C3×C4#12711yescharacteristic
462#67—42no—
463#67—42no—
464#67—42no—
465#67—42no—
466C2×Dic3—24no—
467C2×Dic3—24no—
468C2×Dic3—24no—
469C2×Dic3—22no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—44no—
477C2×Dic3—42no—
478D12—22no—
479D12—22no—
480D12—41no—
481D12—41no—
482C4×D3—42no—
483C4×D3—42no—
484C4×D3—42no—
485C4×D3—42no—
486Dic6—22no—
487Dic6—22no—
488Dic6—41no—
489Dic6—41no—
490C3×C8—42no—
491C3⋊C8—24no—
492C24—21no—
493C24—61no—
494C24D3×D411yescharacteristic
495#41—22no—
496#41—22no—
497#41—22no—
498#41—22no—
499#41—22no—
500#41—22no—
501#41—22no—
502#41—22no—
503#41—41no—
504#41—41no—
505#41—41no—
506#41—41no—
507#41—41no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—62no—
512#41—62no—
513#41—62no—
514#41—62no—
515#41—62no—
516#41—62no—
517#41—62no—
518#41—62no—
519#41—121no—
520#41—121no—
521#41—121no—
522#41—121no—
523#41—121no—
524#41—121no—
525#41—121no—
526#41—121no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—32no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8(C2×D3)⋊C412yescomplemented
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—32no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—62no—
552C2×D4—62no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—121no—
559C2×D4—121no—
560C2×D4—121no—
561C2×D4—121no—
562C2×D4(C2×D3)⋊C412yescomplemented
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—61no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—124no—
579C22×C4—121no—
580C22×C4—121no—
581C22×C4—121no—
582C22×C4—121no—
583C22×C4C2×C4×D311yescharacteristic
584C22×C4C2×D1211yescharacteristic
585C22×C4#23511yescharacteristic
586C22×C4#23511yescharacteristic
587C22×C4D3×D411yescharacteristic
588C22×C4D3×D411yescharacteristic
589C22×C4D3×D411yescharacteristic
590C22×C4D3×D411yescharacteristic
591C22×C4D3×D411yescharacteristic
592C22×C4#23711yescharacteristic
593C22×C4#23711yescharacteristic
594C22×C4C2×#6711yescharacteristic
595C22×C4C2×#6711yescharacteristic
596C22×C4C2×#6711yescharacteristic
597Q16—68no—
598SD16—68no—
599SD16—68no—
600D8—68no—
601M16—22no—
602M16—22no—
603M16—41no—
604M16—41no—
605M16—62no—
606M16—62no—
607M16—62no—
608M16—62no—
609C2×C8—22no—
610C2×C8—34no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—62no—
614C2×C8—62no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—121no—
618C4⋊C4—121no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—128no—
622C22⋊C4—128no—
623C22⋊C4—121no—
624C22⋊C4—121no—
625C42—22no—
626C42—22no—
627C42—62no—
628C42—62no—
629C42—121no—
630C42—121no—
631C42—121no—
632C42—121no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—44no—
641C22×C3—42no—
642C22×C3—82no—
643C22×C3—82no—
644C22×C3#38611yescharacteristic
645C22×C3#38611yescharacteristic
646C22×C3#39011yescharacteristic
647C22×C3#39211yescharacteristic
648C22×C3#39211yescharacteristic
649C22×C3#39211yescharacteristic
650C22×C3#39411yescharacteristic
651C2×D3—44no—
652C2×D3—42no—
653C2×D3—82no—
654C2×D3—82no—
655C3×C4—42no—
656C3×C4—82no—
657C3×C4#37911yescharacteristic
658C3×C4#38611yescharacteristic
659C3×C4#38611yescharacteristic
660C3×C4#39011yescharacteristic
661C3×C4#39211yescharacteristic
662C3×C4#39411yescharacteristic
663C3×C4#39411yescharacteristic
664C3×C4#39411yescharacteristic
665Dic3—42no—
666Dic3—44no—
667Dic3—82no—
668C23—22no—
669C23—42no—
670C23—44no—
671C23—41no—
672C23—41no—
673C23—62no—
674C23—124no—
675C23—121no—
676C23—121no—
677C23#67⋊C411yescharacteristic
678C23#88211yescharacteristic
679C23#88411yescharacteristic
680C23#88411yescharacteristic
681C23#93711yescharacteristic
682C23#93911yescharacteristic
683C23#94011yescharacteristic
684Q8—22no—
685Q8—22no—
686Q8—41no—
687Q8—41no—
688Q8—62no—
689Q8—62no—
690Q8—121no—
691Q8—121no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—41no—
699D4—41no—
700D4—62no—
701D4—62no—
702D4—122no—
703D4—122no—
704D4—122no—
705D4—122no—
706D4—121no—
707D4—121no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—64no—
718C2×C4—64no—
719C2×C4—64no—
720C2×C4—62no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—124no—
732C2×C4—122no—
733C2×C4D3×C22⋊C411yescharacteristic
734C2×C4D3×C22⋊C411yescharacteristic
735C2×C4#67⋊C411yescharacteristic
736C2×C4#88211yescharacteristic
737C2×C4#88211yescharacteristic
738C2×C4#88311yescharacteristic
739C2×C4#88311yescharacteristic
740C2×C4#88411yescharacteristic
741C2×C4#88411yescharacteristic
742C2×C4#88511yescharacteristic
743C2×C4#88511yescharacteristic
744C2×C4#88611yescharacteristic
745C2×C4C2×(C2×D3)⋊C411yescharacteristic
746C2×C4C4×#6711yescharacteristic
747C2×C4C4×#6711yescharacteristic
748C2×C4#92911yescharacteristic
749C2×C4#93011yescharacteristic
750C2×C4#93011yescharacteristic
751C2×C4#93711yescharacteristic
752C2×C4#93711yescharacteristic
753C2×C4#93711yescharacteristic
754C2×C4#93811yescharacteristic
755C2×C4#93811yescharacteristic
756C2×C4#93911yescharacteristic
757C2×C4#93911yescharacteristic
758C2×C4#93911yescharacteristic
759C2×C4#94011yescharacteristic
760C2×C4#95311yescharacteristic
761C8—42no—
762C8—64no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—82no—
770C2×C3#143811yescharacteristic
771C2×C3#201012yes—
772D3—82no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—44no—
781C22—42no—
782C22—82no—
783C22—82no—
784C22—124no—
785C22—122no—
786C22—242no—
787C22—242no—
788C22#495611yescharacteristic
789C22#495711yescharacteristic
790C22#495811yescharacteristic
791C22#495911yescharacteristic
792C22#496011yescharacteristic
793C22#496011yescharacteristic
794C22#522311yescharacteristic
795C4—42no—
796C4—82no—
797C4—124no—
798C4—122no—
799C4—242no—
800C4#495511yescharacteristic
801C4#495611yescharacteristic
802C4#495711yescharacteristic
803C4#495911yescharacteristic
804C4#496111yescharacteristic
805C4#496111yescharacteristic
806C4#521311yescharacteristic
807C4#522311yescharacteristic
808C3#1104111yescharacteristic, complemented, Sylow
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—82no—
816C2—242no—
817C2#7040612yes—
818C2#7155011yescharacteristic
subgroupG/H
centerC2×C4#940
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#421C2
socleC22×C3#392
prime radicalC2×#5822C2
cosocleC23×C3×C4C23
hypercenterC2×#421D3
hypocenterC3#11041
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×C3×#421C2semidirect
3. #84086C2semidirect
4. C2×#5139C2semidirect
5. #82228C2semidirect
6. #71979C2semidirect
7. C2×#4531C2semidirect
17. #5822C4semidirect
43. C2×#421D3semidirect
192. C2×C3×Q8C22⋊C4semidirect
204. C2×C3×D4C22⋊C4semidirect
260. C2×D12C22⋊C4semidirect
272. C2×Dic6C22⋊C4semidirect
308. C2×C3⋊C8C22⋊C4semidirect
538. C2×Q8(C2×D3)⋊C4semidirect
562. C2×D4(C2×D3)⋊C4semidirect
808. C3#11041semidirect

Maximal subgroups

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

subgroupindex
C2×#58222
C2×C3×#4212
#840862
C2×#51392
#822282
#719792
C2×#45312
#110413