Finite Group Databasebeta

← #10846020

Subgroups — #10846020

Order 768.

1070 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#468C211yesmaximal, characteristic, complemented
2C2×#5162C211yesmaximal, characteristic, complemented
3C2×#5128C211yesmaximal, characteristic, complemented
4#82780C211yesmaximal, characteristic, complemented
5#82667C211yesmaximal, characteristic
6C2×#4780C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#71989C211yesmaximal, characteristic, complemented
9#71695C211yesmaximal, characteristic, complemented
10#71685C211yesmaximal, characteristic, complemented
11#70635C211yesmaximal, characteristic, complemented
12#70615C211yesmaximal, characteristic, complemented
13#70271C211yesmaximal, characteristic, complemented
14#70225C211yesmaximal, characteristic, complemented
15Dic3×#102C211yesmaximal, characteristic, complemented
16#25393—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C2×#939—21no—
24C2×#938C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26C22×#214C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C2×#897C2211yescharacteristic
31C3×#468—24no—
32C2×C3×#107C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37#5222—21no—
38C2×#832C2211yescharacteristic
39#5212C2211yescharacteristic
40C2×#830C2211yescharacteristic
41#5162—24no—
42#5128—24no—
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#816C2211yescharacteristic
45C2×#816C2211yescharacteristic
46C2×Dic3⋊C8C2211yescharacteristic
47C2×C8×Dic3C2211yescharacteristic
48#4993—21no—
49#4987C2211yescharacteristic
50#4975—21no—
51#4975C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4959—21no—
56#4957—21no—
57#4949—21no—
58#4942—21no—
59#4780—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#468D311yescharacteristic, complemented
66C2×#461—31no—
67C2×#436—31no—
68#2542—31no—
69#2537—31no—
70#2036—31no—
71#2036—31no—
72#2000—31no—
73#2000—31no—
74#1956—31no—
75#1947—31no—
76#1894—31no—
77#1894—31no—
78C4×#102—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C23×Dic3—21no—
86C22×C4×D3C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—41no—
91C2×C3×M16—22no—
92C2×C3×M16—22no—
93C2×C3×M16—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—41no—
98C3×#121—22no—
99C3×#121—41no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217D411yescharacteristic
110#946—22no—
111#946—41no—
112#944—22no—
113#944—22no—
114#939—44no—
115#938—22no—
116#938—41no—
117D4×Dic3—22no—
118D4×Dic3—22no—
119C2×#214—22no—
120C2×#214—22no—
121C2×#214—41no—
122C4×#67—22no—
123C4×#67—22no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4D411yescharacteristic
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132#924—22no—
133#924—41no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4D411yescharacteristic
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×ΓL(1,𝔽25)—22no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)—41no—
148#897—22no—
149#897—41no—
150C3×#107—22no—
151C3×#103—22no—
152C3×#102D414yescomplemented
153#835—22no—
154#835—41no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#830—22no—
160(C2×D3)⋊C8—22no—
161#816—22no—
162#816—22no—
163Dic3⋊C8D414yescomplemented
164C8×Dic3—22no—
165#810—41no—
166#807—22no—
167C22×SD16—31no—
168C22×SD16C2×D311yescharacteristic
169C22×M16—31no—
170C22×M16C2×D311yescharacteristic
171C2×C4⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8C2×D311yescharacteristic
176C2×#121—31no—
177C2×#121—61no—
178C2×#121C2×D311yescharacteristic
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181#468—24no—
182#468—64no—
183#461—64no—
184#436—64no—
185C2×#107—31no—
186C2×#107C2×D311yescharacteristic
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102C2×D311yescharacteristic
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×C4×C8—31no—
199#399—61no—
200#399—61no—
201#394—61no—
202#394—61no—
203#390—61no—
204#384—31no—
205#384—61no—
206#380—31no—
207#380—31no—
208#380—61no—
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
216C23×D3C2×D411yescharacteristic
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—81no—
231C2×C3×D4C2×D412yes—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C2×#67—22no—
244C2×#67—22no—
245C2×#67—22no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—81no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—42no—
254C22×Dic3—42no—
255C22×Dic3—42no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C3×SD16—44no—
272C3×M16—44no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8C2×D412yes—
278C2×C3×C8C2×D412yes—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—42no—
283C3×C4⋊C4C2×D412yes—
284C3×C22⋊C4—42no—
285C3×C22⋊C4—42no—
286#217—22no—
287#217—42no—
288#217—42no—
289#217—42no—
290#217—42no—
291#214—44no—
292(C2×D3)⋊C4—22no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—42no—
302C4⋊Dic3#4112yes—
303Dic3⋊C4—22no—
304Dic3⋊C4—42no—
305Dic3⋊C4—42no—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308Dic3⋊C4—42no—
309Dic3⋊C4—81no—
310C4×Dic3—42no—
311C4×Dic3C2×D412yes—
312C4×Dic3#4112yes—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8C2×D412yes—
319ΓL(1,𝔽25)—44no—
320C22×Q8—31no—
321C22×Q8C22×D311yescharacteristic
322C22×D4—21no—
323C22×D4—31no—
324C22×D4—61no—
325C22×D4C22×D311yescharacteristic
326C23×C4—31no—
327C23×C4—61no—
328C23×C4C22×D311yescharacteristic
329C2×SD16—22no—
330C2×SD16—22no—
331C2×SD16—41no—
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—121no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—41no—
338C2×M16—62no—
339C2×M16—62no—
340C2×M16—121no—
341C22×C8—31no—
342C22×C8—31no—
343C22×C8C22×D311yescharacteristic
344C22×C8C22×D311yescharacteristic
345C4⋊Q8—62no—
346C4⋊Q8—62no—
347C22⋊Q8—22no—
348C22⋊Q8—41no—
349C22⋊Q8—62no—
350C22⋊Q8—62no—
351C22⋊Q8—62no—
352C22⋊Q8—121no—
353C22⋊Q8—121no—
354C22⋊Q8—121no—
355#121—22no—
356#121—41no—
357#121—62no—
358#121—121no—
359#121—124no—
360C4×D4—62no—
361C4×D4—62no—
362C4×D4—62no—
363C4×D4—62no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4C22×D311yescharacteristic
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C42—31no—
390C2×C42—61no—
391#107—22no—
392#107—62no—
393C4⋊C8—34no—
394#103—22no—
395#103—62no—
396#103—62no—
397#103—62no—
398#103—121no—
399#103—121no—
400#102—62no—
401#102#6714yescomplemented
402C22⋊C8—62no—
403C22⋊C8—62no—
404C4×C8—62no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3—21no—
409C23×C3—22no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3C22×D411yescharacteristic
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×D4—22no—
435C3×D4—22no—
436C3×D4—41no—
437C3×D4—41no—
438C3×D4—84no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4H(5,𝔽2)11yescharacteristic
460C2×C3×C4H(5,𝔽2)11yescharacteristic
461#67—44no—
462#67—84no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—84no—
481C2×Dic3#12112yes—
482C2×Dic3#12112yes—
483C2×Dic3AGL(1,ℤ/8)12yes—
484C2×Dic3#13712yes—
485C4×D3—41no—
486C4×D3—41no—
487C4×D3—41no—
488C4×D3—41no—
489Dic6—41no—
490Dic6—41no—
491Dic6—41no—
492Dic6—41no—
493C3×C8—22no—
494C3×C8—22no—
495C3⋊C8—22no—
496C3⋊C8—41no—
497C24—21no—
498C24—31no—
499C24D3×D411yescharacteristic
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—62no—
520C2×D4—62no—
521C2×D4—62no—
522C2×D4—81no—
523C2×D4—122no—
524C2×D4—122no—
525C2×D4—241no—
526C2×D4C2×#6712yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—31no—
537C22×C4—31no—
538C22×C4—31no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—122no—
550C22×C4—122no—
551C22×C4—122no—
552C22×C4D3×D411yescharacteristic
553C22×C4C23×D311yescharacteristic
554SD16—44no—
555SD16—124no—
556M16—44no—
557M16—124no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—32no—
563C2×C8—61no—
564C2×C8—61no—
565C2×C8—61no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8D3×D412yes—
569C2×C8C2×#6712yes—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—32no—
574C4⋊C4—42no—
575C4⋊C4—62no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—122no—
582C4⋊C4—122no—
583C4⋊C4—122no—
584C4⋊C4—122no—
585C4⋊C4—122no—
586C4⋊C4—122no—
587C4⋊C4—241no—
588C4⋊C4C2×#6712yes—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—62no—
592C22⋊C4—62no—
593C22⋊C4—122no—
594C22⋊C4—122no—
595C22⋊C4—122no—
596C22⋊C4—122no—
597C22⋊C4—122no—
598C22⋊C4—122no—
599C22⋊C4—122no—
600C42—32no—
601C42—32no—
602C42—122no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—42no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3C2×#12111yescharacteristic
618C22×C3D4211yescharacteristic
619C22×C3#54611yescharacteristic
620C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
621C22×C3C2×#13711yescharacteristic
622C22×C3#57711yescharacteristic
623C22×C3#57811yescharacteristic
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C3×C4—41no—
632C3×C4—42no—
633C3×C4—81no—
634C3×C4—81no—
635C3×C4#53211yescharacteristic
636C3×C4#54011yescharacteristic
637C3×C4D4211yescharacteristic
638C3×C4#55011yescharacteristic
639Dic3—22no—
640Dic3—42no—
641Dic3—41no—
642Dic3—81no—
643Dic3—81no—
644Dic3—81no—
645Dic3#46814yescomplemented
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—22no—
652C23—21no—
653C23—21no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—61no—
661C23—61no—
662C23—61no—
663C23—61no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23C2×D3×D411yescharacteristic
668Q8—41no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—121no—
673Q8—121no—
674Q8—121no—
675Q8—121no—
676D4—22no—
677D4—22no—
678D4—41no—
679D4—41no—
680D4—84no—
681D4—124no—
682D4—244no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—32no—
688C2×C4—32no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—62no—
708C2×C4—61no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—244no—
725C2×C4C2×D3×D411yescharacteristic
726C2×C4#100411yescharacteristic
727C2×C4#100411yescharacteristic
728C2×C4D3×#4111yescharacteristic
729C2×C4D3×#4111yescharacteristic
730C2×C4C22×#6711yescharacteristic
731C8—22no—
732C8—22no—
733C8—62no—
734C8—121no—
735C2×C3—81no—
736C2×C3—82no—
737C2×C3#242811yescharacteristic
738C2×C3C2×#46811yescharacteristic
739C2×C3#306311yescharacteristic
740C2×C3#327211yescharacteristic
741C2×C3#327611yescharacteristic
742C2×C3#332911yescharacteristic
743C2×C3#333011yescharacteristic
744D3—81no—
745C22—41no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22D3×#12111yescharacteristic
767C22#561011yescharacteristic
768C22D3×AGL(1,ℤ/8)11yescharacteristic
769C22#577511yescharacteristic
770C22D3×#13711yescharacteristic
771C22#577911yescharacteristic
772C22D4×#6711yescharacteristic
773C4—34no—
774C4—41no—
775C4—42no—
776C4—62no—
777C4—81no—
778C4—81no—
779C4—122no—
780C4—121no—
781C4—241no—
782C4—241no—
783C4—241no—
784C4#559911yescharacteristic
785C4#561511yescharacteristic
786C4D4×#6711yescharacteristic
787C4#583211yescharacteristic
788C3#2539311yescharacteristic, complemented, Sylow
789C2—81no—
790C2—82no—
791C2—241no—
792C2D3×#46811yescharacteristic
793C2#8081011yescharacteristic
794C2#8084211yescharacteristic
795C2#8084611yescharacteristic
796C2#8265011yescharacteristic
797C2#8395811yescharacteristic
798C2#8399611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#468C2
socleC23×C3C22×D4
prime radical#82667C2
hypercenterC2×#468D3
hypocenterC3#25393
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×C3×#468C2semidirect
2. C2×#5162C2semidirect
3. C2×#5128C2semidirect
4. #82780C2semidirect
6. C2×#4780C2semidirect
7. #72054C2semidirect
8. #71989C2semidirect
9. #71695C2semidirect
10. #71685C2semidirect
11. #70635C2semidirect
12. #70615C2semidirect
13. #70271C2semidirect
14. #70225C2semidirect
15. Dic3×#102C2semidirect
65. C2×#468D3semidirect
152. C3×#102D4semidirect
163. Dic3⋊C8D4semidirect
401. #102#67semidirect
645. Dic3#468semidirect
788. C3#25393semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4682
C2×#51622
C2×#51282
#827802
#826672
C2×#47802
#720542
#719892
#716952
#716852
#706352
#706152
#702712
#702252
Dic3×#1022
#253933