Finite Group Databasebeta

← #10702075

Subgroups — #10702075

Order 768.

1310 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5748C211yesmaximal, characteristic
2C2×#5139C211yesmaximal, characteristic, complemented
3C2×#5133C211yesmaximal, characteristic, complemented
4#82270C211yesmaximal, characteristic, complemented
5C2×#5006C211yesmaximal, characteristic, complemented
6C2×C3×#344C211yesmaximal, characteristic, complemented
7#71985C211yesmaximal, characteristic, complemented
8#11036—31nomaximal, Sylow
9C22×#235C2211yescharacteristic
10C22×#235C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C22×C3×M16C2211yescharacteristic
13C2×C3×#117C2211yescharacteristic
14C2×#926C2211yescharacteristic
15C22×C4⋊Dic3C2211yescharacteristic
16#5748—22no—
17#5748—22no—
18#5748—22no—
19#5748C414yescomplemented
20C2×#909—21no—
21C2×#909—21no—
22C2×#908—21no—
23C2×#908—21no—
24C2×#904—22no—
25#5139—22no—
26#5139—22no—
27C2×#825—22no—
28#5133—22no—
29#5133—22no—
30C2×#821—21no—
31C2×#816—21no—
32#5006—22no—
33#5006—22no—
34#4987—22no—
35#4958—22no—
36C2×#806—22no—
37#4939—21no—
38#4929—21no—
39C3×#344—22no—
40#4551—22no—
41C2×#575—31no—
42C2×#421—31no—
43C2×#417—31no—
44C2×#410—31no—
45#2311—31no—
46C2×#344D311yescharacteristic, complemented
47#1736—31no—
48C23×C3×C4C2311yescharacteristic
49C22×#67—21no—
50C22×#67—21no—
51C23×Dic3—21no—
52C2×#235—21no—
53C2×#235—21no—
54C2×#235—21no—
55C2×#235—21no—
56C2×#235—21no—
57C2×#235—21no—
58C2×#235—21no—
59C2×#235—21no—
60C2×#235—21no—
61C2×#235—21no—
62C2×#235—21no—
63C2×#235—21no—
64C2×#235—21no—
65C2×#235—21no—
66C2×#235—21no—
67C2×#235—21no—
68C2×#235—21no—
69C2×#235—21no—
70C2×#235—21no—
71C2×#235—21no—
72C2×#235C2×C412yes—
73C2×#235C2×C412yes—
74C2×#235D412yes—
75C2×#235D412yes—
76C22×D12D411yescharacteristic
77C22×D12D411yescharacteristic
78C22×C4×D3—21no—
79C22×C4×D3—21no—
80C22×Dic6D411yescharacteristic
81C22×Dic6D411yescharacteristic
82C2×C3×M16—21no—
83C2×C3×M16—21no—
84C2×C3×M16—21no—
85C2×C3×M16—21no—
86C2×C3×M16—21no—
87C2×C3×M16—21no—
88C2×C3×M16—21no—
89C2×C3×M16—21no—
90C2×C3×M16—21no—
91C2×C3×M16C2×C412yes—
92C2×C3×M16D412yes—
93C2×C3×M16D412yes—
94C22×C3×C8—21no—
95C22×C3×C8D412yes—
96C3×#117—21no—
97C3×#117—21no—
98C3×#117—21no—
99C3×#117—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C22⋊C4D412yes—
102C2×C3×C42—21no—
103C2×#217—21no—
104C2×(C2×D3)⋊C4—24no—
105#926—21no—
106#926—21no—
107#926—21no—
108#926D412yes—
109C2×C4⋊Dic3—21no—
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3—21no—
112C2×C4⋊Dic3—21no—
113C2×C4⋊Dic3—21no—
114C2×C4⋊Dic3—21no—
115C2×C4⋊Dic3D412yes—
116C2×C4×Dic3—21no—
117#909—24no—
118#909—24no—
119#909—24no—
120#909—24no—
121#908—24no—
122#908—24no—
123#908—24no—
124#908—24no—
125C2×Dic12—22no—
126#904—28no—
127#904—28no—
128C2×D24—22no—
129C2×#204—22no—
130C2×#204—22no—
131C3⋊#95—24no—
132#825—28no—
133#821—24no—
134#816—24no—
135#806—28no—
136C22×#41—31no—
137C22×#41—31no—
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×M16C2×D311yescharacteristic
148C22×M16C2×D311yescharacteristic
149C2×#117—31no—
150C2×#117C2×D311yescharacteristic
151C22×C4⋊C4—31no—
152#421—62no—
153#421—62no—
154C2×#104—62no—
155#417—62no—
156#417—62no—
157C2×#103—61no—
158C2×#102—61no—
159#410—62no—
160#410—62no—
161C2×#99—62no—
162#391—61no—
163#390—61no—
164#386—62no—
165#380—62no—
166#344—22no—
167#340—62no—
168C24×C3C2×D411yescharacteristic
169C23×D3—21no—
170C23×D3—21no—
171C22×C3×C4—22no—
172C22×C3×C4C22×C411yescharacteristic
173C22×C3×C4C2×D411yescharacteristic
174C22×C3×C4C2×D411yescharacteristic
175C22×C3×C4C2×D411yescharacteristic
176C22×C3×C4C2×D411yescharacteristic
177C22×C3×C4C2×D411yescharacteristic
178C22×C3×C4C2×D411yescharacteristic
179C22×C3×C4C2×D411yescharacteristic
180C22×C3×C4C2×D411yescharacteristic
181C22×C3×C4C2×D411yescharacteristic
182C22×C3×C4#4111yescharacteristic
183C22×C3×C4#4111yescharacteristic
184C22×C3×C4#4111yescharacteristic
185C22×C3×C4#4111yescharacteristic
186C2×#67—22no—
187C2×#67—22no—
188C2×#67—22no—
189C2×#67—22no—
190C2×#67—41no—
191C2×#67—41no—
192C2×#67—41no—
193C2×#67—41no—
194C2×#67—41no—
195C2×#67—41no—
196C2×#67—41no—
197C2×#67—41no—
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3—22no—
201C22×Dic3—41no—
202C22×Dic3—41no—
203C22×Dic3—41no—
204C22×Dic3—82no—
205#235—22no—
206#235—22no—
207#235—22no—
208#235—22no—
209#235—22no—
210#235—22no—
211#235—22no—
212#235—22no—
213#235—22no—
214#235—22no—
215#235—22no—
216#235—22no—
217#235—22no—
218#235—22no—
219#235—22no—
220#235—22no—
221#235—41no—
222#235—41no—
223#235—41no—
224#235—41no—
225#235—41no—
226#235—41no—
227#235—41no—
228#235—41no—
229#235—41no—
230#235—41no—
231#235—41no—
232#235—41no—
233#235—41no—
234#235—41no—
235#235—41no—
236#235—41no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12C22⋊C412yes—
248C2×D12C22⋊C412yescomplemented
249C2×C4×D3—22no—
250C2×C4×D3—22no—
251C2×C4×D3—22no—
252C2×C4×D3—22no—
253C2×C4×D3—41no—
254C2×C4×D3—41no—
255C2×C4×D3—41no—
256C2×C4×D3—41no—
257C2×C4×D3—41no—
258C2×C4×D3—41no—
259C2×C4×D3—41no—
260C2×C4×D3—41no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6C22⋊C412yes—
272C2×Dic6C22⋊C412yescomplemented
273C3×M16—22no—
274C3×M16—22no—
275C3×M16—22no—
276C3×M16—22no—
277C3×M16—22no—
278C3×M16—22no—
279C3×M16—41no—
280C3×M16—41no—
281C2×C3×C8—22no—
282C2×C3×C8—22no—
283C2×C3×C8—22no—
284C2×C3×C8—41no—
285C2×C3×C8—41no—
286C2×C3×C8C22⋊C414yescomplemented
287C3×C4⋊C4—41no—
288C3×C4⋊C4—41no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—22no—
291C3×C42—41no—
292C3×C42—41no—
293#217—22no—
294#217—41no—
295(C2×D3)⋊C4—84no—
296C4⋊Dic3—22no—
297C4⋊Dic3—22no—
298C4⋊Dic3—22no—
299C4⋊Dic3—41no—
300C4⋊Dic3—41no—
301C4⋊Dic3—41no—
302C4×Dic3—22no—
303C4×Dic3—41no—
304Dic12—28no—
305D24—28no—
306#204—28no—
307#204—28no—
308C2×#41—32no—
309C2×#41—32no—
310C2×#41—32no—
311C2×#41—32no—
312C2×#41—61no—
313C2×#41—61no—
314C2×#41—61no—
315C2×#41—61no—
316C2×#41—61no—
317C2×#41—61no—
318C2×#41—61no—
319C2×#41—61no—
320C2×#41—61no—
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×#41—61no—
332C22×Q8—31no—
333C22×Q8—31no—
334C22×D4—31no—
335C22×D4—31no—
336C22×D4—61no—
337C22×D4—61no—
338C23×C4—61no—
339C23×C4—61no—
340C23×C4—61no—
341C23×C4C22×D311yescharacteristic
342#137—64no—
343#137—64no—
344#137—64no—
345#137—64no—
346AGL(1,ℤ/8)—64no—
347AGL(1,ℤ/8)—64no—
348AGL(1,ℤ/8)—64no—
349AGL(1,ℤ/8)—64no—
350#135—68no—
351#135—68no—
352C2×Q16—62no—
353C2×SD16—62no—
354C2×SD16—62no—
355C2×D8—62no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16C4×D312yes—
366C2×M16D1212yes—
367C2×M16#6712yes—
368C22×C8—21no—
369C22×C8D1212yes—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—32no—
375#117—61no—
376#117—61no—
377#117—61no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—64no—
388C2×C22⋊C4D1212yes—
389C2×C42—21no—
390C2×C42—61no—
391#104—68no—
392#103—64no—
393#102—64no—
394#99—68no—
395#95—64no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3C4×D411yescharacteristic
399C23×C3#12011yescharacteristic
400C23×C3#12011yescharacteristic
401C23×C3#12111yescharacteristic
402C23×C3#12111yescharacteristic
403C23×C3#12111yescharacteristic
404C23×C3#12711yescharacteristic
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—41no—
410C22×D3—41no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—81no—
414C22×D3—81no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4C2×C22⋊C411yescharacteristic
419C2×C3×C4C2×C22⋊C411yescharacteristic
420C2×C3×C4C2×C22⋊C411yescharacteristic
421C2×C3×C4C4×D411yescharacteristic
422C2×C3×C4C4×D411yescharacteristic
423C2×C3×C4C4×D411yescharacteristic
424C2×C3×C4#12011yescharacteristic
425C2×C3×C4#12011yescharacteristic
426C2×C3×C4#12011yescharacteristic
427C2×C3×C4#12011yescharacteristic
428C2×C3×C4#12011yescharacteristic
429C2×C3×C4#12011yescharacteristic
430C2×C3×C4#12111yescharacteristic
431C2×C3×C4#12111yescharacteristic
432C2×C3×C4#12111yescharacteristic
433C2×C3×C4#12111yescharacteristic
434C2×C3×C4#12111yescharacteristic
435C2×C3×C4#12111yescharacteristic
436C2×C3×C4#12111yescharacteristic
437C2×C3×C4#12111yescharacteristic
438C2×C3×C4#12111yescharacteristic
439C2×C3×C4#12311yescharacteristic
440C2×C3×C4#12311yescharacteristic
441C2×C3×C4#12311yescharacteristic
442C2×C3×C4#12311yescharacteristic
443C2×C3×C4#12411yescharacteristic
444C2×C3×C4#12411yescharacteristic
445C2×C3×C4#12711yescharacteristic
446#67—42no—
447#67—42no—
448#67—42no—
449#67—42no—
450#67—42no—
451#67—42no—
452#67—42no—
453#67—42no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—44no—
461C2×Dic3—42no—
462C2×Dic3—42no—
463C2×Dic3—81no—
464C2×Dic3—81no—
465C2×Dic3—82no—
466C2×Dic3—82no—
467D12—22no—
468D12—22no—
469D12—22no—
470D12—22no—
471D12—41no—
472D12—41no—
473D12—41no—
474D12—41no—
475C4×D3—42no—
476C4×D3—42no—
477C4×D3—42no—
478C4×D3—42no—
479C4×D3—42no—
480C4×D3—42no—
481C4×D3—42no—
482C4×D3—42no—
483Dic6—22no—
484Dic6—22no—
485Dic6—22no—
486Dic6—22no—
487Dic6—41no—
488Dic6—41no—
489Dic6—41no—
490Dic6—41no—
491C3×C8—24no—
492C3×C8—42no—
493C24—61no—
494C24—61no—
495C24C2×D1211yescharacteristic
496#41—62no—
497#41—62no—
498#41—62no—
499#41—62no—
500#41—62no—
501#41—62no—
502#41—62no—
503#41—62no—
504#41—62no—
505#41—62no—
506#41—62no—
507#41—62no—
508#41—62no—
509#41—62no—
510#41—62no—
511#41—62no—
512#41—121no—
513#41—121no—
514#41—121no—
515#41—121no—
516#41—121no—
517#41—121no—
518#41—121no—
519#41—121no—
520#41—121no—
521#41—121no—
522#41—121no—
523#41—121no—
524#41—121no—
525#41—121no—
526#41—121no—
527#41—121no—
528C2×Q8—32no—
529C2×Q8—32no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×D4—32no—
541C2×D4—32no—
542C2×D4—62no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—121no—
557C2×D4—121no—
558C2×D4—121no—
559C2×D4—121no—
560C2×D4—121no—
561C2×D4—121no—
562C2×D4—121no—
563C2×D4—121no—
564C22×C4—22no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—121no—
573C22×C4—121no—
574C22×C4—121no—
575C22×C4—121no—
576C22×C4—121no—
577C22×C4—121no—
578C22×C4—121no—
579C22×C4—121no—
580C22×C4—121no—
581C22×C4—121no—
582C22×C4—121no—
583C22×C4—242no—
584C22×C4C2×C4×D311yescharacteristic
585C22×C4C2×D1211yescharacteristic
586C22×C4C2×D1211yescharacteristic
587C22×C4#23511yescharacteristic
588C22×C4#23511yescharacteristic
589C22×C4D3×D411yescharacteristic
590C22×C4D3×D411yescharacteristic
591C22×C4D3×D411yescharacteristic
592C22×C4D3×D411yescharacteristic
593C22×C4D3×D411yescharacteristic
594C22×C4D3×D411yescharacteristic
595C22×C4#23911yescharacteristic
596C22×C4#23911yescharacteristic
597C22×C4C2×#6711yescharacteristic
598Q16—68no—
599SD16—68no—
600SD16—68no—
601D8—68no—
602M16—22no—
603M16—22no—
604M16—22no—
605M16—22no—
606M16—22no—
607M16—22no—
608M16—41no—
609M16—41no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8(C2×D3)⋊C414yescomplemented
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—62no—
619C4⋊C4—62no—
620C4⋊C4—62no—
621C4⋊C4—121no—
622C4⋊C4—121no—
623C4⋊C4—121no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—62no—
627C22⋊C4—121no—
628C22⋊C4—244no—
629C42—41no—
630C42—41no—
631C42—62no—
632C42—121no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3#38611yescharacteristic
644C22×C3#38611yescharacteristic
645C22×C3#39011yescharacteristic
646C22×C3#39211yescharacteristic
647C22×C3#39211yescharacteristic
648C22×C3#39211yescharacteristic
649C22×C3#39411yescharacteristic
650C2×D3—44no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—82no—
654C2×D3—82no—
655C2×D3—81no—
656C2×D3—81no—
657C2×D3—81no—
658C2×D3—81no—
659C2×D3—82no—
660C3×C4—82no—
661C3×C4#37911yescharacteristic
662C3×C4#38611yescharacteristic
663C3×C4#38611yescharacteristic
664C3×C4#39011yescharacteristic
665C3×C4#39211yescharacteristic
666C3×C4#39411yescharacteristic
667C3×C4#39411yescharacteristic
668C3×C4#39411yescharacteristic
669Dic3—42no—
670Dic3—42no—
671Dic3—82no—
672Dic3—82no—
673C23—41no—
674C23—41no—
675C23—62no—
676C23—62no—
677C23—122no—
678C23—122no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23—241no—
684C23—241no—
685C23C4×D1211yescharacteristic
686C23#87411yescharacteristic
687C23#88211yescharacteristic
688C23#88211yescharacteristic
689C23#89511yescharacteristic
690C23#89511yescharacteristic
691C23#93011yescharacteristic
692Q8—62no—
693Q8—62no—
694Q8—62no—
695Q8—62no—
696Q8—121no—
697Q8—121no—
698Q8—121no—
699Q8—121no—
700D4—62no—
701D4—62no—
702D4—62no—
703D4—62no—
704D4—122no—
705D4—122no—
706D4—122no—
707D4—122no—
708D4—122no—
709D4—122no—
710D4—122no—
711D4—122no—
712D4—121no—
713D4—121no—
714D4—121no—
715D4—121no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—124no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—242no—
737C2×C4—242no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4C4×D1211yescharacteristic
741C2×C4#87511yescharacteristic
742C2×C4D3×C22⋊C411yescharacteristic
743C2×C4D3×C22⋊C411yescharacteristic
744C2×C4#88211yescharacteristic
745C2×C4#88211yescharacteristic
746C2×C4#88211yescharacteristic
747C2×C4#88211yescharacteristic
748C2×C4#88411yescharacteristic
749C2×C4#88411yescharacteristic
750C2×C4#88411yescharacteristic
751C2×C4#88411yescharacteristic
752C2×C4#89311yescharacteristic
753C2×C4#89311yescharacteristic
754C2×C4#89411yescharacteristic
755C2×C4#89411yescharacteristic
756C2×C4#89411yescharacteristic
757C2×C4#89411yescharacteristic
758C2×C4#89511yescharacteristic
759C2×C4#89511yescharacteristic
760C2×C4#89511yescharacteristic
761C2×C4#89511yescharacteristic
762C2×C4C2×(C2×D3)⋊C411yescharacteristic
763C2×C4#93011yescharacteristic
764C2×C4#93711yescharacteristic
765C2×C4#93711yescharacteristic
766C2×C4#94011yescharacteristic
767C2×C4#94711yescharacteristic
768C8—24no—
769C8—42no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3#143811yescharacteristic
777C2×C3#200811yescharacteristic
778C2×C3#200911yescharacteristic
779D3—82no—
780D3—82no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—124no—
792C22—122no—
793C22—122no—
794C22—242no—
795C22—242no—
796C22—242no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22—241no—
801C22#466511yescharacteristic
802C22#466511yescharacteristic
803C22#467111yescharacteristic
804C22#467111yescharacteristic
805C22#493911yescharacteristic
806C22#496011yescharacteristic
807C22#499111yescharacteristic
808C4—82no—
809C4—122no—
810C4—122no—
811C4—242no—
812C4—242no—
813C4#466511yescharacteristic
814C4#466511yescharacteristic
815C4#467211yescharacteristic
816C4#467211yescharacteristic
817C4#495511yescharacteristic
818C4#496011yescharacteristic
819C4#498811yescharacteristic
820C4#499111yescharacteristic
821C3#1103611yescharacteristic, complemented, Sylow
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—21no—
828C2—242no—
829C2—242no—
830C2#6902811yescharacteristic
831C2#6903111yescharacteristic
832C2#6942611yescharacteristic
subgroupG/H
centerC22#4671
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#344C2
socleC22×C3#392
prime radicalC2×#5748C2
cosocleC23×C3×C4C23
hypercenterC2×#344D3
hypocenterC3#11036
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
2. C2×#5139C2semidirect
3. C2×#5133C2semidirect
4. #82270C2semidirect
5. C2×#5006C2semidirect
6. C2×C3×#344C2semidirect
7. #71985C2semidirect
19. #5748C4semidirect
46. C2×#344D3semidirect
248. C2×D12C22⋊C4semidirect
272. C2×Dic6C22⋊C4semidirect
286. C2×C3×C8C22⋊C4semidirect
615. C2×C8(C2×D3)⋊C4semidirect
821. C3#11036semidirect

Maximal subgroups

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

subgroupindex
C2×#57482
C2×#51392
C2×#51332
#822702
C2×#50062
C2×C3×#3442
#719852
#110363