Finite Group Databasebeta

← #10796843

Subgroups — #10796843

Order 768.

1700 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5745C211yesmaximal, characteristic, complemented
2#85735C211yesmaximal, characteristic
3C2×#5132C211yesmaximal, characteristic, complemented
4#83762C211yesmaximal, characteristic, complemented
5#83762C211yesmaximal, characteristic, complemented
6C2×C3×#344C211yesmaximal, characteristic, complemented
7C2×#4533C211yesmaximal, characteristic, complemented
8#69036C218yesmaximal, complemented
9#20964—31nomaximal, Sylow
10C22×#235C2211yescharacteristic
11C22×#235C2211yescharacteristic
12C22×C3×M16C2211yescharacteristic
13C22×C3×M16C2211yescharacteristic
14C2×C3×#117C2211yescharacteristic
15C22×#208C2211yescharacteristic
16C22×#208C2211yescharacteristic
17#5745—22no—
18#5745—22no—
19#5745—22no—
20#5745C2214yes—
21C2×#907—22no—
22C2×D3×M16—22no—
23C2×#901—22no—
24#5526—21no—
25#5526C412yes—
26#5525—21no—
27#5525C412yes—
28#5524—22no—
29#5524C2214yes—
30#5510—22no—
31#5493C414yes—
32#5477—22no—
33C2×#824—21no—
34#5132—22no—
35#5132C2214yes—
36C2×#823—21no—
37#5129—22no—
38#5129—22no—
39#5126C2214yescomplemented
40#5126C2214yescomplemented
41#5110—22no—
42#5110—22no—
43C3×#344C2214yescomplemented
44#4533C2214yescomplemented
45C2×#568—31no—
46#3449—31no—
47C2×#413—31no—
48#2879—31no—
49#2879—31no—
50#1891—38no—
51C2×#344—31no—
52C2×#344D311yescharacteristic, complemented
53C23×C3×C4C2311yescharacteristic
54C22×#67C2×C412yes—
55C22×#67C2×C412yes—
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×#235—21no—
73C2×#235—21no—
74C2×#235—21no—
75C2×#235—21no—
76C2×#235C2×C412yes—
77C2×#235D412yes—
78C2×#235D412yes—
79C2×#235C2312yes—
80C22×D12C2×C411yescharacteristic
81C22×D12D411yescharacteristic
82C22×C4×D3D412yes—
83C22×C4×D3C2312yes—
84C22×Dic6C2×C411yescharacteristic
85C22×Dic6D411yescharacteristic
86C2×C3×M16—21no—
87C2×C3×M16—21no—
88C2×C3×M16—21no—
89C2×C3×M16—21no—
90C2×C3×M16—21no—
91C2×C3×M16—21no—
92C2×C3×M16—21no—
93C2×C3×M16—21no—
94C2×C3×M16—21no—
95C2×C3×M16D412yescomplemented
96C2×C3×M16C2312yes—
97C2×C3×M16C2312yes—
98C22×C3×C8—21no—
99C22×C3×C8D412yescomplemented
100C3×#117—21no—
101C3×#117—21no—
102C3×#117C2×C412yes—
103C3×#117C2312yes—
104C2×C3×C4⋊C4—21no—
105C2×C3×C22⋊C4C2×C412yes—
106C2×C3×C42—21no—
107#930—28no—
108C2×#208—21no—
109C2×#208—21no—
110C2×#208—21no—
111C2×#208—21no—
112C2×#208—21no—
113C2×#208—21no—
114C2×#208—21no—
115C2×#208—21no—
116C2×#208—21no—
117C2×#208D412yescomplemented
118C2×#208C2312yes—
119C2×#208C2312yes—
120C22×C3⋊C8—21no—
121C22×C3⋊C8D412yescomplemented
122#907—28no—
123#907—28no—
124D3×M16—28no—
125D3×M16—28no—
126#901—28no—
127#901—28no—
128C2×ΓL(1,𝔽25)—24no—
129C2×D3×C8—24no—
130#897—24no—
131#897—24no—
132#895—24no—
133#895—24no—
134#886—24no—
135#886C2×C418yes—
136#882—24no—
137#882C2×C418yes—
138#875—22no—
139#875—22no—
140#874—22no—
141C4×D12—28no—
142#869—22no—
143#824—24no—
144#823—24no—
145(C2×D3)⋊C8—28no—
146(C2×D3)⋊C8—28no—
147C22×#41—31no—
148C22×#41—31no—
149#568—34no—
150#568—62no—
151#568—62no—
152#568—62no—
153C2×#131—62no—
154C2×#131—62no—
155C22×M16—31no—
156C22×M16—31no—
157C22×M16—62no—
158C22×M16C2×D311yescharacteristic
159C22×M16C2×D311yescharacteristic
160#537—62no—
161#536—32no—
162#536—61no—
163#535—32no—
164#535—61no—
165#534—34no—
166#532—62no—
167#525—34no—
168#525—62no—
169C2×#117C2×D311yescharacteristic
170#413—34no—
171#413—62no—
172C2×#101—61no—
173C2×#100—61no—
174#408—62no—
175#408—62no—
176#408—62no—
177#408—62no—
178#407—34no—
179#407—34no—
180#344—34no—
181#344C2×D314yescomplemented
182C24×C3C22×C411yescharacteristic
183C23×D3C22⋊C412yes—
184C23×D3C22×C412yes—
185C22×C3×C4—22no—
186C22×C3×C4C22×C411yescharacteristic
187C22×C3×C4C2×D411yescharacteristic
188C22×C3×C4C2×D411yescharacteristic
189C22×C3×C4C2×D411yescharacteristic
190C22×C3×C4C2×D411yescharacteristic
191C22×C3×C4C2×D411yescharacteristic
192C22×C3×C4C2×D411yescharacteristic
193C22×C3×C4C2×D411yescharacteristic
194C22×C3×C4C2×D411yescharacteristic
195C22×C3×C4#4111yescharacteristic
196C22×C3×C4#4111yescharacteristic
197C22×C3×C4#4111yescharacteristic
198C22×C3×C4#4111yescharacteristic
199C22×C3×C4C2411yescharacteristic
200C2×#67—22no—
201C2×#67—22no—
202C2×#67—22no—
203C2×#67—22no—
204C2×#67—22no—
205C2×#67—22no—
206C2×#67—22no—
207C2×#67—22no—
208C2×#67—22no—
209C2×#67—22no—
210C2×#67C22⋊C414yes—
211C2×#67C22×C414yes—
212C22×Dic3C22⋊C412yes—
213C22×Dic3C22×C412yes—
214#235—22no—
215#235—22no—
216#235—22no—
217#235—22no—
218#235—22no—
219#235—22no—
220#235—22no—
221#235—22no—
222#235—22no—
223#235—22no—
224#235—22no—
225#235—22no—
226#235—22no—
227#235—22no—
228#235—22no—
229#235—22no—
230#235—41no—
231#235—41no—
232#235—41no—
233#235—41no—
234#235—41no—
235#235—41no—
236#235—41no—
237#235—41no—
238#235—41no—
239#235—41no—
240#235—41no—
241#235—41no—
242#235—41no—
243#235—41no—
244#235—41no—
245#235—41no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—28no—
257C2×D12C22⋊C412yes—
258C2×D12C2×D412yes—
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3—22no—
262C2×C4×D3—22no—
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—22no—
266C2×C4×D3—22no—
267C2×C4×D3—22no—
268C2×C4×D3—22no—
269C2×C4×D3C22⋊C414yes—
270C2×C4×D3C2×D414yes—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6—21no—
281C2×Dic6C22⋊C412yes—
282C2×Dic6C2×D412yes—
283C3×M16—22no—
284C3×M16—22no—
285C3×M16—22no—
286C3×M16—22no—
287C3×M16—22no—
288C3×M16—22no—
289C3×M16—41no—
290C3×M16—41no—
291C2×C3×C8—22no—
292C2×C3×C8—22no—
293C2×C3×C8—22no—
294C2×C3×C8—41no—
295C2×C3×C8—41no—
296C2×C3×C8C2×D414yes—
297C3×C4⋊C4—22no—
298C3×C4⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4C22×C414yes—
301C3×C42—22no—
302C3×C42—22no—
303(C2×D3)⋊C4—28no—
304(C2×D3)⋊C4—28no—
305C4⋊Dic3—28no—
306#208—22no—
307#208—22no—
308#208—22no—
309#208—22no—
310#208—22no—
311#208—22no—
312#208—41no—
313#208—41no—
314C2×C3⋊C8—22no—
315C2×C3⋊C8—22no—
316C2×C3⋊C8—22no—
317C2×C3⋊C8—41no—
318C2×C3⋊C8—41no—
319C2×C3⋊C8C2×D414yes—
320ΓL(1,𝔽25)—216no—
321D3×C8—216no—
322C2×#41—32no—
323C2×#41—32no—
324C2×#41—32no—
325C2×#41—32no—
326C2×#41—61no—
327C2×#41—61no—
328C2×#41—61no—
329C2×#41—61no—
330C2×#41—61no—
331C2×#41—61no—
332C2×#41—61no—
333C2×#41—61no—
334C2×#41—61no—
335C2×#41—61no—
336C2×#41—61no—
337C2×#41—61no—
338C2×#41—61no—
339C2×#41—61no—
340C2×#41—61no—
341C2×#41—61no—
342C2×#41—61no—
343C2×#41—61no—
344C2×#41—61no—
345C2×#41—61no—
346C22×Q8—31no—
347C22×Q8—31no—
348C22×D4—32no—
349C22×D4—32no—
350C22×D4—31no—
351C22×D4—31no—
352C23×C4—32no—
353C23×C4—32no—
354C23×C4C22×D311yescharacteristic
355#131—68no—
356#131—68no—
357#131—68no—
358#131—68no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—32no—
369C2×M16—32no—
370C2×M16—32no—
371C2×M16—64no—
372C2×M16—68no—
373C2×M16—68no—
374C2×M16—61no—
375C2×M16—61no—
376C2×M16—61no—
377C2×M16—61no—
378C2×M16—61no—
379C2×M16—61no—
380C2×M16—61no—
381C2×M16—61no—
382C2×M16—61no—
383C2×M16D1212yescomplemented
384C2×M16C22×D312yes—
385C2×M16C22×D312yes—
386C22×C8—21no—
387C22×C8—32no—
388C22×C8—64no—
389C22×C8—61no—
390C22×C8D1212yescomplemented
391C4⋊Q8—62no—
392#127—62no—
393#124—62no—
394#124—62no—
395#123—38no—
396#123—64no—
397C22⋊Q8—64no—
398C22⋊Q8—64no—
399#121—64no—
400#121—64no—
401#121—68no—
402#120—38no—
403#120—64no—
404C4×D4—68no—
405#117—21no—
406#117—21no—
407#117C4×D312yes—
408#117C22×D312yes—
409C2×C4⋊C4—21no—
410C2×C22⋊C4C4×D312yes—
411C2×C42—21no—
412#101—64no—
413#100—64no—
414C22⋊C8—68no—
415C22⋊C8—68no—
416C23×C3—81no—
417C23×C3C2×C22⋊C411yescharacteristic
418C23×C3C2×C22⋊C411yescharacteristic
419C23×C3C4×D411yescharacteristic
420C23×C3C4×D411yescharacteristic
421C23×C3C4×D411yescharacteristic
422C23×C3C4×D411yescharacteristic
423C23×C3C23×C411yescharacteristic
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—82no—
430C22×D3—82no—
431C22×D3C2×C22⋊C414yes—
432C2×C3×C4—24no—
433C2×C3×C4—82no—
434C2×C3×C4C2×C22⋊C411yescharacteristic
435C2×C3×C4C2×C22⋊C411yescharacteristic
436C2×C3×C4C4×D411yescharacteristic
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#12111yescharacteristic
445C2×C3×C4#12111yescharacteristic
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#12311yescharacteristic
453C2×C3×C4#12311yescharacteristic
454C2×C3×C4#12311yescharacteristic
455C2×C3×C4#12311yescharacteristic
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C22×D411yescharacteristic
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462#67—24no—
463#67—24no—
464#67—24no—
465#67—24no—
466#67—42no—
467#67—42no—
468#67—42no—
469#67—42no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3C2×C22⋊C414yes—
476D12—22no—
477D12—22no—
478D12—22no—
479D12—22no—
480D12—41no—
481D12—41no—
482D12—41no—
483D12—41no—
484D12—88no—
485C4×D3—24no—
486C4×D3—24no—
487C4×D3—24no—
488C4×D3—24no—
489C4×D3—42no—
490C4×D3—42no—
491C4×D3—42no—
492C4×D3—42no—
493Dic6—22no—
494Dic6—22no—
495Dic6—22no—
496Dic6—22no—
497Dic6—41no—
498Dic6—41no—
499Dic6—41no—
500Dic6—41no—
501C3×C8—24no—
502C3×C8—42no—
503C3⋊C8—24no—
504C3⋊C8—42no—
505C24—32no—
506C24—32no—
507C24C2×C4×D311yescharacteristic
508#41—62no—
509#41—62no—
510#41—62no—
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—62no—
520#41—62no—
521#41—62no—
522#41—62no—
523#41—62no—
524#41—121no—
525#41—121no—
526#41—121no—
527#41—121no—
528#41—121no—
529#41—121no—
530#41—121no—
531#41—121no—
532#41—121no—
533#41—121no—
534#41—121no—
535#41—121no—
536#41—121no—
537#41—121no—
538#41—121no—
539#41—121no—
540C2×Q8—32no—
541C2×Q8—32no—
542C2×Q8—61no—
543C2×Q8—61no—
544C2×Q8—61no—
545C2×Q8—61no—
546C2×Q8—61no—
547C2×Q8—61no—
548C2×Q8—61no—
549C2×Q8—61no—
550C2×Q8—61no—
551C2×Q8—61no—
552C2×D4—34no—
553C2×D4—34no—
554C2×D4—32no—
555C2×D4—32no—
556C2×D4—68no—
557C2×D4—62no—
558C2×D4—62no—
559C2×D4—62no—
560C2×D4—62no—
561C2×D4—62no—
562C2×D4—62no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4—62no—
566C2×D4—62no—
567C2×D4—61no—
568C2×D4—61no—
569C2×D4—61no—
570C2×D4—61no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C22×C4—22no—
578C22×C4—32no—
579C22×C4—34no—
580C22×C4—34no—
581C22×C4—32no—
582C22×C4—62no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4—62no—
592C22×C4C2×C4×D311yescharacteristic
593C22×C4C2×D1211yescharacteristic
594C22×C4C2×D1211yescharacteristic
595C22×C4#23511yescharacteristic
596C22×C4#23511yescharacteristic
597C22×C4D3×D411yescharacteristic
598C22×C4D3×D411yescharacteristic
599C22×C4D3×D411yescharacteristic
600C22×C4D3×D411yescharacteristic
601C22×C4D3×D411yescharacteristic
602C22×C4D3×D411yescharacteristic
603C22×C4#23911yescharacteristic
604C22×C4#23911yescharacteristic
605C22×C4C23×D311yescharacteristic
606M16—22no—
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—41no—
613M16—41no—
614M16—616no—
615M16—62no—
616M16—62no—
617M16—62no—
618M16—62no—
619M16—62no—
620M16—62no—
621M16—121no—
622M16—121no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—34no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—616no—
630C2×C8—62no—
631C2×C8—62no—
632C2×C8—62no—
633C2×C8—121no—
634C2×C8—121no—
635C2×C8C2×D1214yes—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—68no—
639C22⋊C4—22no—
640C22⋊C4—68no—
641C22⋊C4—68no—
642C22⋊C4C2×C4×D314yes—
643C42—22no—
644C42—22no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3#38611yescharacteristic
653C22×C3#38611yescharacteristic
654C22×C3#38611yescharacteristic
655C22×C3#38611yescharacteristic
656C22×C3C22×C22⋊C411yescharacteristic
657C22×C3C2×C4×D411yescharacteristic
658C22×C3C2×C4×D411yescharacteristic
659C2×D3—24no—
660C2×D3—44no—
661C2×D3—44no—
662C2×D3—44no—
663C2×D3—44no—
664C2×D3—44no—
665C2×D3—42no—
666C2×D3—82no—
667C3×C4—44no—
668C3×C4#38611yescharacteristic
669C3×C4#38611yescharacteristic
670C3×C4#38611yescharacteristic
671C3×C4#38611yescharacteristic
672C3×C4C2×#12011yescharacteristic
673C3×C4C2×#12111yescharacteristic
674C3×C4C2×#12111yescharacteristic
675C3×C4C2×#12311yescharacteristic
676Dic3—24no—
677Dic3—42no—
678C23—34no—
679C23—62no—
680C23—62no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23—81no—
685C23—242no—
686C23—242no—
687C23C4×D1211yescharacteristic
688C23C4×D1211yescharacteristic
689C23D3×C22⋊C411yescharacteristic
690C23D3×C22⋊C411yescharacteristic
691C23#89311yescharacteristic
692C23#89311yescharacteristic
693C23C22×C4×D311yescharacteristic
694Q8—62no—
695Q8—62no—
696Q8—62no—
697Q8—62no—
698Q8—121no—
699Q8—121no—
700Q8—121no—
701Q8—121no—
702D4—64no—
703D4—64no—
704D4—64no—
705D4—64no—
706D4—62no—
707D4—62no—
708D4—62no—
709D4—62no—
710D4—122no—
711D4—122no—
712D4—122no—
713D4—122no—
714D4—121no—
715D4—121no—
716D4—121no—
717D4—121no—
718D4—248no—
719C2×C4—24no—
720C2×C4—34no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—64no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—64no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—82no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4C4×D1211yescharacteristic
736C2×C4C4×D1211yescharacteristic
737C2×C4D3×C22⋊C411yescharacteristic
738C2×C4D3×C22⋊C411yescharacteristic
739C2×C4#88211yescharacteristic
740C2×C4#88211yescharacteristic
741C2×C4#88211yescharacteristic
742C2×C4#88211yescharacteristic
743C2×C4#88411yescharacteristic
744C2×C4#88411yescharacteristic
745C2×C4#88411yescharacteristic
746C2×C4#88411yescharacteristic
747C2×C4#89311yescharacteristic
748C2×C4#89311yescharacteristic
749C2×C4#89411yescharacteristic
750C2×C4#89411yescharacteristic
751C2×C4#89411yescharacteristic
752C2×C4#89411yescharacteristic
753C2×C4#89511yescharacteristic
754C2×C4#89511yescharacteristic
755C2×C4#89511yescharacteristic
756C2×C4#89511yescharacteristic
757C2×C4C22×D1211yescharacteristic
758C2×C4C2×#23511yescharacteristic
759C2×C4C2×D3×D411yescharacteristic
760C2×C4C2×D3×D411yescharacteristic
761C2×C4C2×D3×D411yescharacteristic
762C2×C4C2×#23911yescharacteristic
763C8—24no—
764C8—42no—
765C8—64no—
766C8—122no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3C2×#38611yescharacteristic
775D3—44no—
776D3—82no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—64no—
785C22—124no—
786C22—124no—
787C22—124no—
788C22—124no—
789C22—124no—
790C22—122no—
791C22—242no—
792C22#466511yescharacteristic
793C22#466511yescharacteristic
794C22#466511yescharacteristic
795C22#466511yescharacteristic
796C22C2×C4×D1211yescharacteristic
797C22C2×D3×C22⋊C411yescharacteristic
798C22C2×#89311yescharacteristic
799C4—44no—
800C4—64no—
801C4—122no—
802C4#466511yescharacteristic
803C4#466511yescharacteristic
804C4#466511yescharacteristic
805C4#466511yescharacteristic
806C4C2×#88211yescharacteristic
807C4C2×#88411yescharacteristic
808C4C2×#89411yescharacteristic
809C4C2×#89511yescharacteristic
810C3#2096411yescharacteristic, complemented, Sylow
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—124no—
819C2—242no—
820C2C2×#466511yescharacteristic
subgroupG/H
centerC4C2×#882
commutatorC23×C3C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#344C2
socleC2×C3C2×#386
prime radical#85735C2
cosocleC22×C3×C4C24
hypercenterC2×#344D3
hypocenterC3#20964
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#5745C2semidirect
3. C2×#5132C2semidirect
4. #83762C2semidirect
5. #83762C2semidirect
6. C2×C3×#344C2semidirect
7. C2×#4533C2semidirect
8. #69036C2semidirect
39. #5126C22semidirect
40. #5126C22semidirect
43. C3×#344C22semidirect
44. #4533C22semidirect
52. C2×#344D3semidirect
95. C2×C3×M16D4semidirect
99. C22×C3×C8D4semidirect
117. C2×#208D4semidirect
121. C22×C3⋊C8D4semidirect
181. #344C2×D3semidirect
383. C2×M16D12semidirect
390. C22×C8D12semidirect
810. C3#20964semidirect

Maximal subgroups

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

subgroupindex
C2×#57452
#857352
C2×#51322
#837622
C2×C3×#3442
C2×#45332
#690362
#209643