Finite Group Databasebeta

← #10846066

Subgroups — #10846066

Order 768.

1118 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
1#82779C211yesmaximal, characteristic, complemented
2C2×#5049C211yesmaximal, characteristic, complemented
3C2×#4883C211yesmaximal, characteristic, complemented
4C2×#4819C211yesmaximal, characteristic, complemented
5C2×#4728C211yesmaximal, characteristic, complemented
6#73935C211yesmaximal, characteristic, complemented
7C3×#2036C211yesmaximal, characteristic, complemented
8#70615C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70270C211yesmaximal, characteristic, complemented
11#70227C211yesmaximal, characteristic, complemented
12#69961C211yesmaximal, characteristic, complemented
13#69517C211yesmaximal, characteristic, complemented
14#68822C211yesmaximal, characteristic, complemented
15#68782C211yesmaximal, characteristic, complemented
16#25397—31nomaximal, Sylow
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×#947C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C2×#930C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C22×D24C2211yescharacteristic
26C22×D3×C8C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×#884—21no—
31C2×C3×#107C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×C22⋊C8C2211yescharacteristic
35C3×#380C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×#815C2211yescharacteristic
41C2×Dic3⋊C8C2211yescharacteristic
42#5049—24no—
43#4993—21no—
44#4988—21no—
45#4987C2211yescharacteristic
46#4975C2211yescharacteristic
47Dic3×C4⋊C4C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4960—21no—
53#4959—21no—
54#4957—21no—
55#4883—24no—
56#4819—24no—
57#4728—24no—
58#4672—21no—
59#4667—21no—
60C3×#340C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#466—31no—
66C2×#463—31no—
67C2×#435—31no—
68#2540—31no—
69#2537—31no—
70#2036D311yescharacteristic, complemented
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1959—31no—
75#1947—31no—
76#1895—31no—
77#1892—31no—
78#1762—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C22×#67D411yescharacteristic
84C22×D12—21no—
85C22×D12—21no—
86C22×D12C2311yescharacteristic
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—41no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×#217D411yescharacteristic
101#947—22no—
102#947—22no—
103#946—22no—
104#946—41no—
105C2×#215—22no—
106C2×#215—22no—
107C2×#215—41no—
108#930—22no—
109#930—22no—
110#930—41no—
111#930—41no—
112C4×#67—22no—
113C4×#67—22no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4D411yescharacteristic
130C2×C4×Dic3—21no—
131C2×C4×Dic3C2311yescharacteristic
132C2×#208—22no—
133C2×#208—22no—
134C2×#208—41no—
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C2×D24—22no—
138C2×D24—22no—
139C2×D24—41no—
140C2×D3×C8—22no—
141C2×D3×C8—22no—
142C2×D3×C8—41no—
143#895—22no—
144#895—22no—
145#895—41no—
146#895—41no—
147#893—22no—
148#893—22no—
149#884—44no—
150C3×#107—22no—
151C3×#103—22no—
152C3×#103—41no—
153C3×C22⋊C8—22no—
154C3×#95—21no—
155#835—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#821—22no—
159#821—41no—
160(C2×D3)⋊C8—22no—
161#815—22no—
162Dic3⋊C8D414yescomplemented
163#809—22no—
164#809—22no—
165#809D414yescomplemented
166#807—22no—
167C22×SD16—31no—
168C22×D8—31no—
169C22×M16—31no—
170C23×C8—31no—
171C2×#124—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—61no—
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181#468—64no—
182#466—64no—
183#463—64no—
184#435—64no—
185C2×#107—31no—
186C2×#107C2×D311yescharacteristic
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8C2×D311yescharacteristic
198C2×#97—31no—
199#399—61no—
200#394—61no—
201#394—61no—
202#392—61no—
203#390—61no—
204#390—61no—
205#384—31no—
206#380—31no—
207#380—61no—
208#380C2×D311yescharacteristic
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214C24×C3C2×D411yescharacteristic
215C23×D3—21no—
216C23×D3—21no—
217C23×D3C2×D411yescharacteristic
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C2×#67—22no—
237C2×#67—22no—
238C2×#67—41no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—81no—
244C2×#67—81no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—42no—
262C2×D12—42no—
263C2×D12—42no—
264C2×D12—42no—
265C2×D12—81no—
266C2×D12—81no—
267C2×D12C2×D412yes—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—42no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8C2×D412yes—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—42no—
289C3×C4⋊C4C2×D412yes—
290C3×C22⋊C4—42no—
291C3×C22⋊C4—42no—
292#217—22no—
293#215—44no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3#4112yes—
308Dic3⋊C4—22no—
309Dic3⋊C4—42no—
310Dic3⋊C4—42no—
311Dic3⋊C4—81no—
312C4×Dic3—81no—
313C4×Dic3C2×D412yes—
314C4×Dic3#4112yes—
315#208—44no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8C2×D412yes—
321C2×C3⋊C8C2×D412yes—
322D24—44no—
323D3×C8—44no—
324C22×Q8C22×D311yescharacteristic
325C22×D4—31no—
326C22×D4—31no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4—61no—
332C23×C4—31no—
333C23×C4—61no—
334C23×C4C22×D311yescharacteristic
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—121no—
338C2×D8—62no—
339C2×D8—62no—
340C2×D8—121no—
341C2×M16—62no—
342C2×M16—62no—
343C2×M16—121no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8—62no—
347C22×C8—62no—
348C22×C8—121no—
349C22×C8C22×D311yescharacteristic
350C22×C8C22×D311yescharacteristic
351#124—62no—
352#124—62no—
353C22⋊Q8—22no—
354C22⋊Q8—41no—
355C22⋊Q8—62no—
356C22⋊Q8—121no—
357#121—62no—
358#121—62no—
359#121—62no—
360#121—62no—
361#121—124no—
362#121—121no—
363#121—121no—
364#121—121no—
365#121—121no—
366C4×D4—62no—
367C4×D4—62no—
368C4×D4—62no—
369C4×D4—62no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C42—31no—
394C2×C42—61no—
395#107—22no—
396#107—62no—
397C4⋊C8—34no—
398#103—22no—
399#103—41no—
400#103—62no—
401#102—34no—
402#102—62no—
403#102—62no—
404#102—62no—
405#102—121no—
406C22⋊C8—22no—
407C22⋊C8—62no—
408#97—62no—
409#95—21no—
410#95—61no—
411#95—61no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3C22×D411yescharacteristic
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—22no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3AGL(1,ℤ/8)12yes—
441C3×Q8—41no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
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×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4H(5,𝔽2)11yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470#67—44no—
471#67—84no—
472#67—84no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3#12112yes—
487C2×Dic3#12112yes—
488D12—22no—
489D12—22no—
490D12—41no—
491D12—41no—
492D12—41no—
493D12—41no—
494D12—41no—
495D12—41no—
496D12—84no—
497D12—84no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—41no—
501C4×D3—41no—
502C4×D3—84no—
503C3×C8—22no—
504C3×C8—41no—
505C3⋊C8—22no—
506C3⋊C8—22no—
507C24—31no—
508C24—61no—
509C24—61no—
510C24D3×D411yescharacteristic
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×D4—32no—
518C2×D4—62no—
519C2×D4—62no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—121no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—241no—
541C2×D4—241no—
542C2×D4—241no—
543C2×D4—241no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—122no—
566C22×C4—122no—
567C22×C4—122no—
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—124no—
571D8—124no—
572M16—124no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—32no—
579C2×C8—32no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—124no—
585C2×C8D3×D412yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—32no—
592C4⋊C4—42no—
593C4⋊C4—62no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—122no—
598C4⋊C4—122no—
599C4⋊C4—241no—
600C4⋊C4D3×D412yes—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—62no—
604C22⋊C4—62no—
605C22⋊C4—122no—
606C22⋊C4—122no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—32no—
615C42—32no—
616C42—241no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3C2×#12111yescharacteristic
625C22×C3D4211yescharacteristic
626C22×C3#54611yescharacteristic
627C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
628C22×C3#57511yescharacteristic
629C22×C3#57611yescharacteristic
630C22×C3#57811yescharacteristic
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—81no—
642C2×D3—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C2×D3—81no—
647C2×D3—81no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C3×C4—41no—
653C3×C4—42no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4—81no—
657C3×C4#53211yescharacteristic
658C3×C4#54011yescharacteristic
659C3×C4D4211yescharacteristic
660C3×C4#55011yescharacteristic
661Dic3—22no—
662Dic3—22no—
663Dic3—41no—
664Dic3—42no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—32no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—62no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23C2×D3×D411yescharacteristic
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—41no—
699D4—62no—
700D4—62no—
701D4—124no—
702D4—121no—
703D4—121no—
704D4—121no—
705D4—121no—
706D4—121no—
707D4—121no—
708D4—244no—
709D4—244no—
710D4—244no—
711D4—244no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—32no—
717C2×C4—32no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—62no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—244no—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4#100411yescharacteristic
754C2×C4D3×#4111yescharacteristic
755C2×C4D3×#4111yescharacteristic
756C2×C4#100911yescharacteristic
757C8—22no—
758C8—41no—
759C8—62no—
760C8—62no—
761C2×C3—81no—
762C2×C3#242811yescharacteristic
763C2×C3#305511yescharacteristic
764C2×C3#306111yescharacteristic
765C2×C3#326411yescharacteristic
766C2×C3#326911yescharacteristic
767C2×C3#330811yescharacteristic
768C2×C3#331911yescharacteristic
769D3—42no—
770D3—82no—
771D3—161no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—62no—
780C22—62no—
781C22—62no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—122no—
787C22—122no—
788C22—122no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22#559011yescharacteristic
801C22D3×#12111yescharacteristic
802C22#565411yescharacteristic
803C22#576611yescharacteristic
804C22#576911yescharacteristic
805C22D3×AGL(1,ℤ/8)11yescharacteristic
806C22#577711yescharacteristic
807C4—41no—
808C4—42no—
809C4—62no—
810C4—62no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—121no—
815C4—122no—
816C4—241no—
817C4#559911yescharacteristic
818C4#560911yescharacteristic
819C4#566311yescharacteristic
820C4#566811yescharacteristic
821C3#2539711yescharacteristic, complemented, Sylow
822C2—81no—
823C2—122no—
824C2—242no—
825C2—481no—
826C2#7690311yescharacteristic
827C2#8012011yescharacteristic
828C2#8020511yescharacteristic
829C2#8076111yescharacteristic
830C2#8080511yescharacteristic
831C2#8147311yescharacteristic
832C2#8152811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2036C2
socleC23×C3C22×D4
hypercenter#2036D3
hypocenterC3#25397
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
1. #82779C2semidirect
2. C2×#5049C2semidirect
3. C2×#4883C2semidirect
4. C2×#4819C2semidirect
5. C2×#4728C2semidirect
6. #73935C2semidirect
7. C3×#2036C2semidirect
8. #70615C2semidirect
9. #70272C2semidirect
10. #70270C2semidirect
11. #70227C2semidirect
12. #69961C2semidirect
13. #69517C2semidirect
14. #68822C2semidirect
15. #68782C2semidirect
70. #2036D3semidirect
162. Dic3⋊C8D4semidirect
165. #809D4semidirect
821. C3#25397semidirect

Maximal subgroups

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

subgroupindex
#827792
C2×#50492
C2×#48832
C2×#48192
C2×#47282
#739352
C3×#20362
#706152
#702722
#702702
#702272
#699612
#695172
#688222
#687822
#253973