Finite Group Databasebeta

← #10944272

Subgroups — #10944272

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
2#82834C211yesmaximal, characteristic, complemented
3C2×#5049C211yesmaximal, characteristic, complemented
4C2×#4812C211yesmaximal, characteristic, complemented
5C2×#4807C211yesmaximal, characteristic, complemented
6#74048C211yesmaximal, characteristic
7C3×#1894C211yesmaximal, characteristic, complemented
8#71990C211yesmaximal, characteristic, complemented
9#70271C211yesmaximal, characteristic, complemented
10#70270C211yesmaximal, characteristic, complemented
11#69513C211yesmaximal, characteristic, complemented
12#68885C211yesmaximal, characteristic, complemented
13#68883C211yesmaximal, characteristic, complemented
14#68870C211yesmaximal, characteristic, complemented
15#68869C211yesmaximal, characteristic, complemented
16#32935—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C22×#215C2211yescharacteristic, complemented
23C2×#930C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C2×D3×M16—24no—
26C2×D3×M16—24no—
27C2×D3×M16—24no—
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C22×D3×C8C2211yescharacteristic
31C22×D3×C8C2211yescharacteristic
32C2×#895C2211yescharacteristic
33C2×#895C2211yescharacteristic
34C2×#882—21no—
35C2×C3×#103C2211yescharacteristic, complemented
36C2×C3×#103C2211yescharacteristic, complemented
37C3×#380C2211yescharacteristic
38C2×#835C2211yescharacteristic, complemented
39#5212C2211yescharacteristic
40C2×#821C2211yescharacteristic, complemented
41C2×#821C2211yescharacteristic, complemented
42#5049—24no—
43#4989—21no—
44#4989—21no—
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47#4987C2211yescharacteristic
48#4987C2211yescharacteristic
49C2×#809C2211yescharacteristic, complemented
50C2×#808C2211yescharacteristic, complemented
51C2×#807C2211yescharacteristic, complemented
52C2×#807C2211yescharacteristic, complemented
53#4958—21no—
54#4955—21no—
55#4946—21no—
56#4812—24no—
57#4807—24no—
58#4665—21no—
59#4665—21no—
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62#4551C2211yescharacteristic, complemented
63#4551C2211yescharacteristic, 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#1894D311yescharacteristic, complemented
76#1893—31no—
77#1892—31no—
78#1809—31no—
79#1809—31no—
80#1808—31no—
81C24×D3D411yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C23×Dic3D411yescharacteristic
86C22×D12—21no—
87C22×D12—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3—22no—
90C22×C4×D3—22no—
91C22×C4×D3—22no—
92C22×C4×D3—22no—
93C22×C4×D3—22no—
94C22×C4×D3—22no—
95C22×C4×D3D411yescharacteristic
96C22×C4×D3D411yescharacteristic
97C22×C4×D3C2311yescharacteristic
98C22×C4×D3C2311yescharacteristic
99C2×C3×M16—22no—
100C2×C3×M16—22no—
101C2×C3×M16—22no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×#217—21no—
113#946—22no—
114#946—22no—
115#946—22no—
116#946—22no—
117C2×#215—22no—
118C2×#215—22no—
119C2×#215—22no—
120#930—22no—
121#930—22no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×#208—22no—
137C2×#208—22no—
138C2×#208D414yescomplemented
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141D3×M16—232no—
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)—22no—
144C2×ΓL(1,𝔽25)—22no—
145C2×ΓL(1,𝔽25)—22no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)D414yescomplemented
148C2×D3×C8—22no—
149C2×D3×C8—22no—
150C2×D3×C8—22no—
151C2×D3×C8—22no—
152C2×D3×C8—22no—
153C2×D3×C8D414yescomplemented
154#895—22no—
155#895—22no—
156#895—22no—
157#895—22no—
158#882—44no—
159C3×#103—22no—
160C3×#103—22no—
161C3×#95—21no—
162#835—22no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#821—22no—
169#821—22no—
170#809—22no—
171#808—22no—
172#807—22no—
173#807—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⋊Q8C2×D311yescharacteristic
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×#107—31no—
197C2×#106—31no—
198C2×#103—31no—
199C2×#103C2×D311yescharacteristic, complemented
200C2×#103C2×D311yescharacteristic, complemented
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#380—31no—
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
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D412yes—
250C22×C3×C4#4112yes—
251C22×C3×C4C2411yescharacteristic
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3C2×D411yescharacteristic
262C22×Dic3C2×D411yescharacteristic
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—42no—
270C2×D12—42no—
271C2×D12—42no—
272C2×D12—42no—
273C2×D12—42no—
274C2×D12—42no—
275C2×C4×D3—28no—
276C2×C4×D3—28no—
277C2×C4×D3—28no—
278C2×C4×D3—28no—
279C2×C4×D3—22no—
280C2×C4×D3—22no—
281C2×C4×D3—22no—
282C2×C4×D3—22no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—22no—
292C2×C4×D3—22no—
293C2×C4×D3C2×D412yes—
294C2×C4×D3C2×D412yes—
295C2×C4×D3#4112yes—
296C2×C4×D3#4112yes—
297C3×M16—28no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
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—42no—
311C3×C22⋊C4—42no—
312C3×C22⋊C4—42no—
313#217—42no—
314#215—44no—
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—21no—
329C4⋊Dic3—21no—
330Dic3⋊C4—42no—
331Dic3⋊C4—42no—
332#208—28no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8C2×D412yes—
336C2×C3⋊C8C2×D412yes—
337C2×C3⋊C8C2×D412yes—
338C2×C3⋊C8C2×D412yes—
339ΓL(1,𝔽25)—28no—
340ΓL(1,𝔽25)—28no—
341D3×C8—28no—
342D3×C8—28no—
343C25—31no—
344C22×Q8C22×D311yescharacteristic
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—22no—
367C2×M16—34no—
368C2×M16—34no—
369C2×M16—62no—
370C2×M16—62no—
371C2×M16—62no—
372C2×M16—62no—
373C2×M16—62no—
374C2×M16—62no—
375C2×M16—632no—
376C2×M16—62no—
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—22no—
388C22⋊Q8—22no—
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—21no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4—61no—
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—62no—
422#107—62no—
423#106—62no—
424#103—22no—
425#103—22no—
426#103—62no—
427#102—62no—
428#102—62no—
429#102—62no—
430#95—21no—
431#95—61no—
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—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×Q8—41no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
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—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4#12112yes—
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C22×D411yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499C2×C3×C4C2×#4111yescharacteristic
500C2×C3×C4C2×#4111yescharacteristic
501#67—84no—
502C2×Dic3—28no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3#12112yes—
517C2×Dic3#12112yes—
518D12—41no—
519D12—41no—
520D12—41no—
521D12—41no—
522D12—84no—
523D12—84no—
524C4×D3—28no—
525C4×D3—28no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—22no—
529C4×D3—22no—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—22no—
534C3×C8—22no—
535C3×C8—22no—
536C3⋊C8—22no—
537C3⋊C8#12014yescomplemented
538C24—31no—
539C24—31no—
540C24—62no—
541C24—62no—
542C24—62no—
543C24—62no—
544C24—62no—
545C24—61no—
546C24—121no—
547C24—121no—
548C24D3×D411yescharacteristic
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
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×C4#23512yes—
609C22×C4D3×D411yescharacteristic
610C22×C4D3×D412yes—
611C22×C4C23×D311yescharacteristic
612SD16—124no—
613M16—28no—
614M16—68no—
615M16—68no—
616M16—68no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—32no—
622C2×C8—32no—
623C2×C8—32no—
624C2×C8—32no—
625C2×C8—68no—
626C2×C8—68no—
627C2×C8—61no—
628C2×C8—61no—
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—42no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
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#88412yes—
743C23C2×D3×D411yescharacteristic
744Q8—41no—
745Q8—41no—
746Q8—41no—
747Q8—41no—
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#88412yes—
800C2×C4C2×#23511yescharacteristic
801C2×C4C2×D3×D411yescharacteristic
802C2×C4C2×D3×D411yescharacteristic
803C2×C4C2×D3×D411yescharacteristic
804C2×C4D3×#4111yescharacteristic
805C2×C4D3×#4111yescharacteristic
806C8—22no—
807C8—22no—
808C8—34no—
809C8—62no—
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×#88411yescharacteristic
851C22D3×#12111yescharacteristic
852C22D3×#12111yescharacteristic
853C22D3×AGL(1,ℤ/8)11yescharacteristic
854C22D3×#13711yescharacteristic
855C22#577711yescharacteristic
856C22#577711yescharacteristic
857C4—22no—
858C4—62no—
859C4—62no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—241no—
865C4—241no—
866C4—241no—
867C4#554711yescharacteristic
868C4#554711yescharacteristic
869C4D3×#12011yescharacteristic
870C4#565611yescharacteristic
871C3#3293511yescharacteristic, complemented, Sylow
872C2—42no—
873C2—64no—
874C2—122no—
875C2—481no—
876C2#7493511yescharacteristic
877C2#7888811yescharacteristic
878C2#7896211yescharacteristic
879C2D3×#46811yescharacteristic
880C2#8080511yescharacteristic
881C2#8090311yescharacteristic
882C2#8090411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1894C2
socleC23×C3C22×D4
prime radical#74048C2
hypercenter#1894D3
hypocenterC3#32935
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
1. C22×D3×M16C2semidirect
2. #82834C2semidirect
3. C2×#5049C2semidirect
4. C2×#4812C2semidirect
5. C2×#4807C2semidirect
7. C3×#1894C2semidirect
8. #71990C2semidirect
9. #70271C2semidirect
10. #70270C2semidirect
11. #69513C2semidirect
12. #68885C2semidirect
13. #68883C2semidirect
14. #68870C2semidirect
15. #68869C2semidirect
22. C22×#215C22semidirect
35. C2×C3×#103C22semidirect
36. C2×C3×#103C22semidirect
38. C2×#835C22semidirect
40. C2×#821C22semidirect
41. C2×#821C22semidirect
49. C2×#809C22semidirect
50. C2×#808C22semidirect
51. C2×#807C22semidirect
52. C2×#807C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. #4551C22semidirect
63. #4551C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
75. #1894D3semidirect
138. C2×#208D4semidirect
147. C2×ΓL(1,𝔽25)D4semidirect
153. C2×D3×C8D4semidirect
199. C2×#103C2×D3semidirect
200. C2×#103C2×D3semidirect
221. #340C2×D3semidirect
222. #340C2×D3semidirect
537. C3⋊C8#120semidirect
693. C2×D3#468semidirect
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
#828342
C2×#50492
C2×#48122
C2×#48072
#740482
C3×#18942
#719902
#702712
#702702
#695132
#688852
#688832
#688702
#688692
#329353