Finite Group Databasebeta

← #10796841

Subgroups — #10796841

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
1#87268C211yesmaximal, characteristic
2C2×#5745C211yesmaximal, characteristic, complemented
3C3×#2879C211yesmaximal, characteristic, complemented
4#84074C211yesmaximal, characteristic, complemented
5C2×#5132C211yesmaximal, characteristic, complemented
6C2×#4559C211yesmaximal, characteristic, complemented
7C2×#4556C211yesmaximal, characteristic, complemented
8#69992C218yesmaximal, complemented
9#20964—31nomaximal, Sylow
10C22×C3×#41C2211yescharacteristic
11C22×#235C2211yescharacteristic
12C22×C3×M16C2211yescharacteristic
13C22×C3×M16C2211yescharacteristic
14#5833—22no—
15#5832—22no—
16#5830—21no—
17#5828—22no—
18#5825—21no—
19#5816C412yes—
20#5805C412yes—
21#5804C414yes—
22#5791C2214yes—
23C2×#926C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C22×#208C2211yescharacteristic
26#5745—22no—
27#5745—22no—
28#5745—22no—
29#5745C2214yes—
30C2×#907—22no—
31C2×D3×M16—22no—
32C2×#901—22no—
33C3×#408—22no—
34C3×#408—22no—
35C3×#407C2214yescomplemented
36#5234—22no—
37#5234—22no—
38#5207C2214yescomplemented
39C2×#824—21no—
40#5132—22no—
41#5132C2214yes—
42C2×#823—21no—
43#4559C2214yescomplemented
44#4556C2214yescomplemented
45C2×#568—31no—
46#3449—31no—
47C2×#413—31no—
48#2879—31no—
49#2879D311yescharacteristic, complemented
50#1891—38no—
51C2×#344—31no—
52C2×#344—31no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41—21no—
57C2×C3×#41—21no—
58C2×C3×#41—21no—
59C2×C3×#41—21no—
60C2×C3×#41—21no—
61C2×C3×#41—21no—
62C2×C3×#41—21no—
63C2×C3×#41—21no—
64C2×C3×#41—21no—
65C22×C3×Q8C2×C411yescharacteristic
66C22×C3×D4C2×C412yes—
67C22×C3×D4C2×C411yescharacteristic
68C23×C3×C4C2312yes—
69C23×C3×C4C2311yescharacteristic
70C22×#67C2×C412yes—
71C2×#235—21no—
72C2×#235—21no—
73C2×#235—21no—
74C2×#235—21no—
75C2×#235—21no—
76C2×#235—21no—
77C2×#235—21no—
78C2×#235—21no—
79C2×#235C2×C412yes—
80C2×#235D412yes—
81C2×#235D412yes—
82C2×#235C2312yes—
83C22×D12D411yescharacteristic
84C22×C4×D3D412yes—
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
100#953C2×C418yes—
101C2×#217C2×C412yes—
102#947—22no—
103#946—24no—
104#944—22no—
105#940—22no—
106#939—28no—
107#938—24no—
108#937—24no—
109#936—22no—
110#935—24no—
111#930—24no—
112#929C2×C418yes—
113C4×#67—28no—
114#926—21no—
115#926—21no—
116#926C2×C412yes—
117#926C2312yes—
118C2×C4⋊Dic3—21no—
119#924—24no—
120C2×C4×Dic3—21no—
121C2×#208—21no—
122C2×#208—21no—
123C2×#208—21no—
124C2×#208—21no—
125C2×#208—21no—
126C2×#208—21no—
127C2×#208—21no—
128C2×#208—21no—
129C2×#208—21no—
130C2×#208D412yescomplemented
131C2×#208C2312yes—
132C2×#208C2312yes—
133C22×C3⋊C8—21no—
134C22×C3⋊C8D412yescomplemented
135#907—28no—
136#907—28no—
137D3×M16—28no—
138D3×M16—28no—
139#901—28no—
140#901—28no—
141C2×ΓL(1,𝔽25)—24no—
142C2×D3×C8—24no—
143C3×C22⋊C8—28no—
144#830—28no—
145#824—24no—
146#823—24no—
147C22×#41—31no—
148C22×#41C2×D311yescharacteristic
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×#117—31no—
170#413—34no—
171#413—62no—
172C2×#101—61no—
173C2×#100—61no—
174#408—22no—
175#408—22no—
176#408—62no—
177#408—62no—
178#407—34no—
179#407C2×D314yescomplemented
180#344—34no—
181#344—34no—
182C24×C3C22×C412yes—
183C24×C3C22×C411yescharacteristic
184C23×D3C22⋊C412yes—
185C3×#41—41no—
186C3×#41—41no—
187C3×#41—41no—
188C3×#41—41no—
189C3×#41—41no—
190C3×#41—41no—
191C3×#41—41no—
192C3×#41—41no—
193C3×#41—41no—
194C3×#41—41no—
195C3×#41—41no—
196C3×#41—41no—
197C3×#41—41no—
198C3×#41—41no—
199C3×#41—41no—
200C3×#41—41no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×D4—22no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4C22×C412yes—
226C22×C3×C4C22×C411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4#4111yescharacteristic
236C22×C3×C4#4111yescharacteristic
237C22×C3×C4#4111yescharacteristic
238C22×C3×C4#4111yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C2×#67—22no—
241C2×#67—22no—
242C2×#67—22no—
243C2×#67—22no—
244C2×#67—28no—
245C2×#67C22⋊C414yes—
246C2×#67C22×C414yes—
247C22×Dic3—22no—
248C22×Dic3C22⋊C412yes—
249#235—22no—
250#235—22no—
251#235—22no—
252#235—22no—
253#235—22no—
254#235—22no—
255#235—22no—
256#235—22no—
257#235—22no—
258#235—22no—
259#235—22no—
260#235—22no—
261#235—22no—
262#235—22no—
263#235—22no—
264#235—22no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12C22⋊C412yes—
270C2×D12C2×D412yes—
271C2×C4×D3—22no—
272C2×C4×D3—22no—
273C2×C4×D3—22no—
274C2×C4×D3—22no—
275C2×C4×D3C22⋊C414yes—
276C2×C4×D3C2×D414yes—
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—
297#217—22no—
298#217—28no—
299#217C22×C414yes—
300(C2×D3)⋊C4—28no—
301C4⋊Dic3—22no—
302C4⋊Dic3—22no—
303Dic3⋊C4—28no—
304C4×Dic3—22no—
305C4×Dic3—22no—
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—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—32no—
335C2×#41—32no—
336C2×#41—32no—
337C2×#41—32no—
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×Q8C4×D311yescharacteristic
348C22×D4—32no—
349C22×D4—31no—
350C22×D4C4×D312yes—
351C22×D4C4×D311yescharacteristic
352C23×C4—32no—
353C23×C4C22×D312yes—
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×M16#6712yescomplemented
384C2×M16C22×D312yes—
385C2×M16C22×D312yes—
386C22×C8—21no—
387C22×C8—32no—
388C22×C8—64no—
389C22×C8—61no—
390C22×C8#6712yescomplemented
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—32no—
406#117—32no—
407#117—61no—
408#117—61no—
409C2×C4⋊C4—61no—
410C2×C22⋊C4—32no—
411C2×C42—61no—
412#101—64no—
413#100—64no—
414C22⋊C8—28no—
415C22⋊C8—68no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—81no—
420C23×C3—82no—
421C23×C3C2×C22⋊C411yescharacteristic
422C23×C3C2×C22⋊C411yescharacteristic
423C23×C3C4×D411yescharacteristic
424C23×C3C4×D411yescharacteristic
425C23×C3C4×D411yescharacteristic
426C23×C3C4×D411yescharacteristic
427C23×C3C23×C411yescharacteristic
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—82no—
431C22×D3C2×C22⋊C414yes—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×Q8—41no—
436C3×D4—42no—
437C3×D4—42no—
438C3×D4—42no—
439C3×D4—42no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—41no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4C2×C22⋊C411yescharacteristic
452C2×C3×C4C2×C22⋊C411yescharacteristic
453C2×C3×C4C4×D411yescharacteristic
454C2×C3×C4C4×D411yescharacteristic
455C2×C3×C4C4×D411yescharacteristic
456C2×C3×C4C4×D411yescharacteristic
457C2×C3×C4#12011yescharacteristic
458C2×C3×C4#12011yescharacteristic
459C2×C3×C4#12011yescharacteristic
460C2×C3×C4#12011yescharacteristic
461C2×C3×C4#12111yescharacteristic
462C2×C3×C4#12111yescharacteristic
463C2×C3×C4#12111yescharacteristic
464C2×C3×C4#12111yescharacteristic
465C2×C3×C4#12111yescharacteristic
466C2×C3×C4#12111yescharacteristic
467C2×C3×C4#12111yescharacteristic
468C2×C3×C4#12111yescharacteristic
469C2×C3×C4#12311yescharacteristic
470C2×C3×C4#12311yescharacteristic
471C2×C3×C4#12311yescharacteristic
472C2×C3×C4#12311yescharacteristic
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479#67—24no—
480#67—24no—
481#67—24no—
482#67—24no—
483#67—88no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—24no—
487C2×Dic3—82no—
488C2×Dic3C2×C22⋊C414yes—
489D12—22no—
490D12—22no—
491D12—22no—
492D12—22no—
493C4×D3—24no—
494C4×D3—24no—
495C4×D3—24no—
496C4×D3—24no—
497Dic6—22no—
498Dic6—22no—
499Dic6—22no—
500Dic6—22no—
501C3×C8—24no—
502C3×C8—42no—
503C3⋊C8—24no—
504C3⋊C8—42no—
505C24—32no—
506C24C2×C4×D312yes—
507C24C2×C4×D311yescharacteristic
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514#41—41no—
515#41—41no—
516#41—41no—
517#41—41no—
518#41—41no—
519#41—41no—
520#41—41no—
521#41—41no—
522#41—41no—
523#41—41no—
524#41—62no—
525#41—62no—
526#41—62no—
527#41—62no—
528#41—62no—
529#41—62no—
530#41—62no—
531#41—62no—
532#41—62no—
533#41—62no—
534#41—62no—
535#41—62no—
536#41—62no—
537#41—62no—
538#41—62no—
539#41—62no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—32no—
547C2×Q8—32no—
548C2×Q8—61no—
549C2×Q8—61no—
550C2×Q8—61no—
551C2×Q8—61no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—34no—
565C2×D4—34no—
566C2×D4—32no—
567C2×D4—32no—
568C2×D4—62no—
569C2×D4—62no—
570C2×D4—62no—
571C2×D4—62no—
572C2×D4—68no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—32no—
584C22×C4—34no—
585C22×C4—34no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—62no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4C2×C4×D312yes—
592C22×C4C2×C4×D311yescharacteristic
593C22×C4#23511yescharacteristic
594C22×C4#23511yescharacteristic
595C22×C4D3×D411yescharacteristic
596C22×C4D3×D411yescharacteristic
597C22×C4D3×D411yescharacteristic
598C22×C4D3×D411yescharacteristic
599C22×C4D3×D411yescharacteristic
600C22×C4D3×D411yescharacteristic
601C22×C4#23711yescharacteristic
602C22×C4#23711yescharacteristic
603C22×C4C2×#6711yescharacteristic
604C22×C4C2×#6711yescharacteristic
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×#6714yes—
636C4⋊C4—68no—
637C4⋊C4—62no—
638C4⋊C4—62no—
639C22⋊C4—34no—
640C22⋊C4—68no—
641C22⋊C4—68no—
642C22⋊C4—62no—
643C42—62no—
644C42—62no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—44no—
653C22×C3—44no—
654C22×C3—44no—
655C22×C3—42no—
656C22×C3#38611yescharacteristic
657C22×C3#38611yescharacteristic
658C22×C3#38611yescharacteristic
659C22×C3#38611yescharacteristic
660C22×C3C22×C22⋊C411yescharacteristic
661C22×C3C2×C4×D411yescharacteristic
662C22×C3C2×C4×D411yescharacteristic
663C2×D3—24no—
664C2×D3—44no—
665C2×D3—44no—
666C2×D3—82no—
667C3×C4—42no—
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—44no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—34no—
682C23—62no—
683C23—62no—
684C23—81no—
685C23—82no—
686C23—242no—
687C23D3×C22⋊C411yescharacteristic
688C23D3×C22⋊C411yescharacteristic
689C23#67⋊C411yescharacteristic
690C23#67⋊C411yescharacteristic
691C23C4×#6711yescharacteristic
692C23C4×#6711yescharacteristic
693C23C22×C4×D311yescharacteristic
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—62no—
699Q8—62no—
700Q8—62no—
701Q8—62no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—64no—
711D4—64no—
712D4—64no—
713D4—64no—
714D4—62no—
715D4—62no—
716D4—62no—
717D4—62no—
718D4—248no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—34no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—64no—
730C2×C4—64no—
731C2×C4—64no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—242no—
735C2×C4D3×C22⋊C411yescharacteristic
736C2×C4D3×C22⋊C411yescharacteristic
737C2×C4#67⋊C411yescharacteristic
738C2×C4#67⋊C411yescharacteristic
739C2×C4#88311yescharacteristic
740C2×C4#88311yescharacteristic
741C2×C4#88311yescharacteristic
742C2×C4#88311yescharacteristic
743C2×C4#88411yescharacteristic
744C2×C4#88411yescharacteristic
745C2×C4#88411yescharacteristic
746C2×C4#88411yescharacteristic
747C2×C4C4×#6711yescharacteristic
748C2×C4C4×#6711yescharacteristic
749C2×C4#93711yescharacteristic
750C2×C4#93711yescharacteristic
751C2×C4#93711yescharacteristic
752C2×C4#93711yescharacteristic
753C2×C4#93811yescharacteristic
754C2×C4#93811yescharacteristic
755C2×C4#93811yescharacteristic
756C2×C4#93811yescharacteristic
757C2×C4C2×#23511yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4C2×D3×D411yescharacteristic
760C2×C4C2×D3×D411yescharacteristic
761C2×C4C2×#23711yescharacteristic
762C2×C4C22×#6711yescharacteristic
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×C3—82no—
775C2×C3C2×#38611yescharacteristic
776D3—44no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—42no—
788C22—64no—
789C22—124no—
790C22—124no—
791C22—242no—
792C22#495611yescharacteristic
793C22#495611yescharacteristic
794C22#495611yescharacteristic
795C22#495611yescharacteristic
796C22C2×D3×C22⋊C411yescharacteristic
797C22C2×#67⋊C411yescharacteristic
798C22C2×C4×#6711yescharacteristic
799C4—42no—
800C4—64no—
801C4—124no—
802C4#495611yescharacteristic
803C4#495611yescharacteristic
804C4#495611yescharacteristic
805C4#495611yescharacteristic
806C4C2×#88311yescharacteristic
807C4C2×#88411yescharacteristic
808C4C2×#93711yescharacteristic
809C4C2×#93811yescharacteristic
810C3#2096411yescharacteristic, complemented, Sylow
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—82no—
819C2—124no—
820C2C2×#495611yescharacteristic
subgroupG/H
centerC4C2×#937
commutatorC23×C3C23×C4
FrattiniC22×C4C23×D3
FittingC3×#2879C2
socleC2×C3C2×#386
prime radical#87268C2
cosocleC22×C3×C4C24
hypercenter#2879D3
hypocenterC3#20964
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2879

Complements

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

NH ≅ G/Ntype
2. C2×#5745C2semidirect
3. C3×#2879C2semidirect
4. #84074C2semidirect
5. C2×#5132C2semidirect
6. C2×#4559C2semidirect
7. C2×#4556C2semidirect
8. #69992C2semidirect
35. C3×#407C22semidirect
38. #5207C22semidirect
43. #4559C22semidirect
44. #4556C22semidirect
49. #2879D3semidirect
95. C2×C3×M16D4semidirect
99. C22×C3×C8D4semidirect
130. C2×#208D4semidirect
134. C22×C3⋊C8D4semidirect
179. #407C2×D3semidirect
383. C2×M16#67semidirect
390. C22×C8#67semidirect
810. C3#20964semidirect

Maximal subgroups

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

subgroupindex
#872682
C2×#57452
C3×#28792
#840742
C2×#51322
C2×#45592
C2×#45562
#699922
#209643