Finite Group Databasebeta

← #10944269

Subgroups — #10944269

Order 768.

1580 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×M16C211yesmaximal, characteristic, complemented
2C2×#5134C211yesmaximal, characteristic, complemented
3C2×#4886C211yesmaximal, characteristic, complemented
4C2×#4864C211yesmaximal, characteristic, complemented
5#74049C211yesmaximal, characteristic, complemented
6#74048C211yesmaximal, characteristic
7C3×#1809C211yesmaximal, characteristic, complemented
8#70630C211yesmaximal, characteristic, complemented
9#70578C211yesmaximal, characteristic, complemented
10#69517C211yesmaximal, characteristic, complemented
11#69516C211yesmaximal, characteristic, complemented
12#68885C211yesmaximal, characteristic, complemented
13#68884C211yesmaximal, characteristic, complemented
14#68883C211yesmaximal, characteristic, complemented
15#68882C211yesmaximal, characteristic, complemented
16#32935—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×#924C2211yescharacteristic
21C22×#208C2211yescharacteristic
22C2×D3×M16—24no—
23C2×D3×M16—24no—
24C2×D3×M16—24no—
25C22×#204C2211yescharacteristic, complemented
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×ΓL(1,𝔽25)C2211yescharacteristic
28C22×D3×C8C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30C2×#897C2211yescharacteristic
31C2×#897C2211yescharacteristic
32C2×#895C2211yescharacteristic
33C2×#895C2211yescharacteristic
34C2×#882—21no—
35C2×C3×#107C2211yescharacteristic, complemented
36C2×C3×#106C2211yescharacteristic, complemented
37C3×#380C2211yescharacteristic
38C3×#380C2211yescharacteristic
39#5134—24no—
40C2×#821C2211yescharacteristic, complemented
41C2×#818C2211yescharacteristic, complemented
42C2×#816C2211yescharacteristic, complemented
43#4987C2211yescharacteristic
44#4987C2211yescharacteristic
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47C2×#810C2211yescharacteristic, complemented
48C2×#810C2211yescharacteristic, complemented
49C2×#809C2211yescharacteristic, complemented
50C2×#809C2211yescharacteristic, complemented
51#4958—21no—
52#4955—21no—
53#4950—21no—
54#4886—24no—
55#4864—24no—
56#4668—21no—
57#4668—21no—
58#4665—21no—
59#4665—21no—
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C23×M16—31no—
67C2×#468—31no—
68C2×#468—31no—
69C2×#465—31no—
70#2848—31no—
71#2847—31no—
72#1895—31no—
73#1895—31no—
74#1894—31no—
75#1894—31no—
76#1893—31no—
77#1892—31no—
78#1809—31no—
79#1809D311yescharacteristic, complemented
80#1808—31no—
81C24×D3D411yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C23×Dic3D411yescharacteristic
85C22×D12—21no—
86C22×D12—21no—
87C22×D12C2311yescharacteristic
88C22×C4×D3—22no—
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3D411yescharacteristic
95C22×C4×D3D411yescharacteristic
96C22×C4×D3C2311yescharacteristic
97C22×C4×D3C2311yescharacteristic
98C22×Dic6C2311yescharacteristic
99C2×C3×M16—22no—
100C2×C3×M16—22no—
101C2×C3×M16D414yescomplemented
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×#217—21no—
111#930—22no—
112#930—22no—
113C2×(C2×D3)⋊C4—21no—
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×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126#924—22no—
127#924—22no—
128C2×Dic3⋊C4—21no—
129C2×#208—22no—
130C2×#208—22no—
131C2×#208—22no—
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134D3×M16—232no—
135C2×#204—22no—
136C2×#204—22no—
137C2×#204—22no—
138C2×ΓL(1,𝔽25)—22no—
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)—22no—
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)D414yescomplemented
144C2×D3×C8—22no—
145C2×D3×C8—22no—
146C2×D3×C8—22no—
147C2×D3×C8—22no—
148C2×D3×C8—22no—
149C2×D3×C8D414yescomplemented
150#897—22no—
151#897—22no—
152#897—22no—
153#897—22no—
154#895—22no—
155#895—22no—
156#895—22no—
157#895—22no—
158#882—44no—
159C3×#107—22no—
160C3×#106—22no—
161C3×#95—21no—
162C3×#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167#821—22no—
168#818—22no—
169#816—22no—
170#810—22no—
171#810—22no—
172#809—22no—
173#809—22no—
174C24×C4—31no—
175C22×SD16—31no—
176C22×M16—31no—
177C22×M16—31no—
178C22×M16—31no—
179C22×M16—64no—
180C22×M16—64no—
181C22×M16—64no—
182C22×M16C2×D311yescharacteristic
183C23×C8—31no—
184C23×C8—31no—
185C2×C22⋊Q8—31no—
186C2×C22⋊Q8—31no—
187C2×C22⋊Q8—31no—
188C2×#121—31no—
189C2×#121—31no—
190C2×#121—31no—
191C2×#120—61no—
192#468—64no—
193#468—64no—
194#465—64no—
195C2×#107—31no—
196C2×#107C2×D311yescharacteristic, complemented
197C2×#106C2×D311yescharacteristic, complemented
198C2×#103—31no—
199C2×#103—31no—
200C2×#103—31no—
201C2×#102—31no—
202C2×#102—31no—
203C2×#102—31no—
204#386—61no—
205#386—61no—
206#386—61no—
207#385—61no—
208#385—61no—
209#385—61no—
210#380—31no—
211#380—31no—
212#380—31no—
213#380—31no—
214#380C2×D311yescharacteristic
215#380C2×D311yescharacteristic
216#379—61no—
217#340—31no—
218#340—31no—
219#340—31no—
220#340—31no—
221#340C2×D311yescharacteristic, complemented
222#340C2×D311yescharacteristic, complemented
223C24×C3C2×D411yescharacteristic
224C23×D3—22no—
225C23×D3—22no—
226C23×D3—22no—
227C23×D3—22no—
228C23×D3—22no—
229C23×D3—21no—
230C23×D3—41no—
231C23×D3—41no—
232C23×D3C2×D411yescharacteristic
233C23×D3C2×D411yescharacteristic
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×C4—21no—
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4#4112yes—
245C22×C3×C4C2411yescharacteristic
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3C2×D411yescharacteristic
256C22×Dic3C2×D411yescharacteristic
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—42no—
264C2×D12—42no—
265C2×D12—42no—
266C2×D12—42no—
267C2×D12—42no—
268C2×D12—42no—
269C2×C4×D3—28no—
270C2×C4×D3—28no—
271C2×C4×D3—28no—
272C2×C4×D3—28no—
273C2×C4×D3—22no—
274C2×C4×D3—22no—
275C2×C4×D3—22no—
276C2×C4×D3—22no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—22no—
286C2×C4×D3—22no—
287C2×C4×D3C2×D412yes—
288C2×C4×D3C2×D412yes—
289C2×C4×D3#4112yes—
290C2×C4×D3#4112yes—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6—21no—
297C3×M16—28no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8C2×D412yes—
301C2×C3×C8C2×D412yes—
302C2×C3×C8C2×D412yes—
303C2×C3×C8C2×D412yes—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314#217—42no—
315(C2×D3)⋊C4—42no—
316(C2×D3)⋊C4—42no—
317(C2×D3)⋊C4—42no—
318(C2×D3)⋊C4—42no—
319(C2×D3)⋊C4—42no—
320(C2×D3)⋊C4—42no—
321(C2×D3)⋊C4—42no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—42no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3—42no—
329C4⋊Dic3—42no—
330Dic3⋊C4—42no—
331#208—28no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8C2×D412yes—
337C2×C3⋊C8C2×D412yes—
338#204—44no—
339ΓL(1,𝔽25)—28no—
340ΓL(1,𝔽25)—28no—
341D3×C8—28no—
342D3×C8—28no—
343C25—31no—
344C22×Q8—31no—
345C22×D4—31no—
346C22×D4—61no—
347C22×D4—61no—
348C22×D4—61no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—62no—
355C23×C4—62no—
356C23×C4—62no—
357C23×C4—62no—
358C23×C4—62no—
359C23×C4—62no—
360C23×C4C22×D311yescharacteristic
361C2×SD16—62no—
362C2×SD16—62no—
363C2×SD16—62no—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—34no—
367C2×M16—62no—
368C2×M16—62no—
369C2×M16—62no—
370C2×M16—62no—
371C2×M16—632no—
372C2×M16—62no—
373C2×M16—62no—
374C2×M16—62no—
375C2×M16—62no—
376C2×M16D1214yescomplemented
377C22×C8—31no—
378C22×C8—31no—
379C22×C8—34no—
380C22×C8—62no—
381C22×C8—62no—
382C22×C8—62no—
383C22×C8—62no—
384C22×C8—62no—
385C22×C8C22×D311yescharacteristic
386C22×C8C22×D311yescharacteristic
387C22⋊Q8—62no—
388C22⋊Q8—62no—
389C22⋊Q8—62no—
390C22⋊Q8—62no—
391C22⋊Q8—62no—
392C22⋊Q8—62no—
393#121—62no—
394#121—62no—
395#121—62no—
396#121—62no—
397#121—62no—
398#121—62no—
399#120—124no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4—61no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4C22×D311yescharacteristic
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421#107—22no—
422#107—62no—
423#106—22no—
424#103—62no—
425#103—62no—
426#103—62no—
427#102—62no—
428#102—62no—
429#102—62no—
430#95—21no—
431#95—21no—
432#95—61no—
433#95—61no—
434#95—61no—
435#95—61no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3#12112yes—
443C23×C3C22×D411yescharacteristic
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—28no—
449C22×D3—21no—
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—44no—
456C22×D3—44no—
457C22×D3—44no—
458C22×D3—44no—
459C22×D3—44no—
460C22×D3—44no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3#12112yes—
469C22×D3#12112yes—
470C22×D3AGL(1,ℤ/8)12yes—
471C22×D3#13712yes—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4#12112yes—
491C2×C3×C4C22×D411yescharacteristic
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C2×#4111yescharacteristic
495C2×C3×C4C2×#4111yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497#67—84no—
498C2×Dic3—28no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3#12112yes—
513C2×Dic3#12112yes—
514D12—41no—
515D12—41no—
516D12—41no—
517D12—41no—
518D12—84no—
519D12—84no—
520C4×D3—28no—
521C4×D3—28no—
522C4×D3—22no—
523C4×D3—22no—
524C4×D3—22no—
525C4×D3—22no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—22no—
529C4×D3—22no—
530Dic6—41no—
531Dic6—41no—
532Dic6—41no—
533Dic6—41no—
534C3×C8—22no—
535C3×C8#12014yescomplemented
536C3⋊C8—22no—
537C3⋊C8—22no—
538C24—31no—
539C24—31no—
540C24—62no—
541C24—62no—
542C24—62no—
543C24—62no—
544C24—62no—
545C24—61no—
546C24—121no—
547C24—121no—
548C24D3×D411yescharacteristic
549C2×Q8—61no—
550C2×Q8—61no—
551C2×Q8—61no—
552C2×Q8—61no—
553C2×Q8—61no—
554C2×Q8—61no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—61no—
560C2×D4—61no—
561C2×D4—122no—
562C2×D4—122no—
563C2×D4—122no—
564C2×D4—122no—
565C2×D4—122no—
566C2×D4—122no—
567C2×D4—122no—
568C2×D4—122no—
569C2×D4—122no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—32no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—68no—
589C22×C4—68no—
590C22×C4—68no—
591C22×C4—68no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4C2×D1212yes—
609C22×C4D3×D411yescharacteristic
610C22×C4#23912yes—
611C22×C4C23×D311yescharacteristic
612SD16—124no—
613M16—28no—
614M16—68no—
615M16—68no—
616M16—68no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—32no—
620C2×C8—32no—
621C2×C8—68no—
622C2×C8—61no—
623C2×C8—61no—
624C2×C8—61no—
625C2×C8—61no—
626C2×C8—68no—
627C2×C8C2×D1212yes—
628C2×C8C2×D1212yes—
629C2×C8D3×D412yes—
630C2×C8D3×D412yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—122no—
644C4⋊C4—122no—
645C4⋊C4—122no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—122no—
649C22⋊C4—122no—
650C22⋊C4—122no—
651C22⋊C4—122no—
652C22⋊C4—122no—
653C22⋊C4—122no—
654C22⋊C4—122no—
655C22⋊C4—122no—
656C22⋊C4—122no—
657C22⋊C4—122no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3C2×#12111yescharacteristic
666C22×C3C2×#12111yescharacteristic
667C22×C3C2×#12111yescharacteristic
668C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
669C22×C3C2×#13711yescharacteristic
670C22×C3#57511yescharacteristic
671C22×C3#57511yescharacteristic
672C2×D3—22no—
673C2×D3—22no—
674C2×D3—22no—
675C2×D3—22no—
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—416no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—81no—
687C2×D3—81no—
688C2×D3—81no—
689C2×D3—81no—
690C2×D3—81no—
691C2×D3—81no—
692C2×D3—81no—
693C2×D3#46814yescomplemented
694C3×C4—22no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—81no—
698C3×C4—81no—
699C3×C4C2×#12011yescharacteristic
700C3×C4#52511yescharacteristic
701C3×C4#52511yescharacteristic
702C3×C4#52511yescharacteristic
703Dic3—22no—
704Dic3—22no—
705Dic3—81no—
706Dic3—81no—
707Dic3—81no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—32no—
715C23—32no—
716C23—32no—
717C23—32no—
718C23—68no—
719C23—61no—
720C23—61no—
721C23—61no—
722C23—61no—
723C23—61no—
724C23—61no—
725C23—61no—
726C23—61no—
727C23—61no—
728C23—61no—
729C23—124no—
730C23—124no—
731C23—124no—
732C23—124no—
733C23—124no—
734C23—124no—
735C23—121no—
736C23—121no—
737C23—121no—
738C23—121no—
739C23—121no—
740C23—121no—
741C23—121no—
742C23#89512yes—
743C23C2×D3×D411yescharacteristic
744Q8—121no—
745Q8—121no—
746Q8—121no—
747Q8—121no—
748D4—121no—
749D4—121no—
750D4—121no—
751D4—121no—
752D4—244no—
753D4—244no—
754D4—244no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—68no—
776C2×C4—68no—
777C2×C4—68no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4#89512yes—
800C2×C4C22×D1211yescharacteristic
801C2×C4C2×D3×D411yescharacteristic
802C2×C4C2×D3×D411yescharacteristic
803C2×C4C2×#23911yescharacteristic
804C2×C4D3×#4111yescharacteristic
805C2×C4D3×#4111yescharacteristic
806C8—22no—
807C8—62no—
808C8—62no—
809C8#88214yescomplemented
810C2×C3—42no—
811C2×C3#284711yescharacteristic
812C2×C3C2×#46811yescharacteristic
813C2×C3#305411yescharacteristic
814C2×C3#305511yescharacteristic
815C2×C3#305511yescharacteristic
816C2×C3#305611yescharacteristic
817C2×C3#305611yescharacteristic
818D3—24no—
819D3—42no—
820D3—161no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—34no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—62no—
830C22—62no—
831C22—62no—
832C22—62no—
833C22—62no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22—62no—
838C22—1216no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—241no—
844C22—241no—
845C22—241no—
846C22—241no—
847C22—241no—
848C22—241no—
849C22—241no—
850C22C2×#89511yescharacteristic
851C22D3×#12111yescharacteristic
852C22D3×#12111yescharacteristic
853C22D3×AGL(1,ℤ/8)11yescharacteristic
854C22#577311yescharacteristic
855C22D3×#13711yescharacteristic
856C22#577711yescharacteristic
857C4—22no—
858C4—62no—
859C4—62no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—241no—
865C4—241no—
866C4—241no—
867C4C2×#88211yescharacteristic
868C4#552411yescharacteristic
869C4#562711yescharacteristic
870C4#562711yescharacteristic
871C3#3293511yescharacteristic, complemented, Sylow
872C2—42no—
873C2—64no—
874C2—122no—
875C2—481no—
876C2#7404811yescharacteristic
877C2#7921111yescharacteristic
878C2#7921211yescharacteristic
879C2D3×#46811yescharacteristic
880C2#8080411yescharacteristic
881C2#8086411yescharacteristic
882C2#8090411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1809C2
socleC23×C3C22×D4
prime radical#74048C2
hypercenter#1809D3
hypocenterC3#32935
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
1. C22×D3×M16C2semidirect
2. C2×#5134C2semidirect
3. C2×#4886C2semidirect
4. C2×#4864C2semidirect
5. #74049C2semidirect
7. C3×#1809C2semidirect
8. #70630C2semidirect
9. #70578C2semidirect
10. #69517C2semidirect
11. #69516C2semidirect
12. #68885C2semidirect
13. #68884C2semidirect
14. #68883C2semidirect
15. #68882C2semidirect
25. C22×#204C22semidirect
35. C2×C3×#107C22semidirect
36. C2×C3×#106C22semidirect
40. C2×#821C22semidirect
41. C2×#818C22semidirect
42. C2×#816C22semidirect
47. C2×#810C22semidirect
48. C2×#810C22semidirect
49. C2×#809C22semidirect
50. C2×#809C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. #4529C22semidirect
63. #4529C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
79. #1809D3semidirect
101. C2×C3×M16D4semidirect
143. C2×ΓL(1,𝔽25)D4semidirect
149. C2×D3×C8D4semidirect
196. C2×#107C2×D3semidirect
197. C2×#106C2×D3semidirect
221. #340C2×D3semidirect
222. #340C2×D3semidirect
376. C2×M16D12semidirect
535. C3×C8#120semidirect
693. C2×D3#468semidirect
809. C8#882semidirect
871. C3#32935semidirect

Maximal subgroups

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

subgroupindex
C22×D3×M162
C2×#51342
C2×#48862
C2×#48642
#740492
#740482
C3×#18092
#706302
#705782
#695172
#695162
#688852
#688842
#688832
#688822
#329353