Finite Group Databasebeta

← #10944266

Subgroups — #10944266

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#82723C211yesmaximal, characteristic
3C2×#5042C211yesmaximal, characteristic, complemented
4C2×#4780C211yesmaximal, characteristic, complemented
5C2×#4778C211yesmaximal, characteristic, complemented
6#74049C211yesmaximal, characteristic, complemented
7C3×#1895C211yesmaximal, characteristic, complemented
8#71989C211yesmaximal, characteristic, complemented
9#70203C211yesmaximal, characteristic, complemented
10#70202C211yesmaximal, characteristic, complemented
11#69513C211yesmaximal, characteristic, complemented
12#68884C211yesmaximal, characteristic, complemented
13#68882C211yesmaximal, characteristic, complemented
14#68870C211yesmaximal, characteristic, complemented
15#68869C211yesmaximal, characteristic, complemented
16#32935—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#937—21no—
23C22×#214C2211yescharacteristic, complemented
24C2×#924C2211yescharacteristic
25C22×#208C2211yescharacteristic
26C2×D3×M16—24no—
27C2×D3×M16—24no—
28C2×D3×M16—24no—
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C22×ΓL(1,𝔽25)C2211yescharacteristic
31C22×D3×C8C2211yescharacteristic
32C22×D3×C8C2211yescharacteristic
33C2×#897C2211yescharacteristic
34C2×#897C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic, complemented
36C2×C3×#102C2211yescharacteristic, complemented
37C3×#380C2211yescharacteristic
38#5220—21no—
39C2×#832C2211yescharacteristic, complemented
40#5212C2211yescharacteristic
41C2×#816C2211yescharacteristic, complemented
42C2×#816C2211yescharacteristic, complemented
43#5042—24no—
44#4987C2211yescharacteristic
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47#4987C2211yescharacteristic
48C2×#810C2211yescharacteristic, complemented
49C2×#808C2211yescharacteristic, complemented
50C2×#807C2211yescharacteristic, complemented
51C2×#807C2211yescharacteristic, complemented
52#4956—21no—
53#4956—21no—
54#4955—21no—
55#4950—21no—
56#4780—24no—
57#4778—24no—
58#4668—21no—
59#4668—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#1895D311yescharacteristic, complemented
74#1894—31no—
75#1894—31no—
76#1893—31no—
77#1892—31no—
78#1809—31no—
79#1809—31no—
80#1808—31no—
81C24×D3D411yescharacteristic
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C23×Dic3D411yescharacteristic
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×M16—22no—
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×#121—22no—
105C3×#121—22no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115#938—22no—
116#938—22no—
117#938—22no—
118#938—22no—
119#937—44no—
120C2×#214—22no—
121C2×#214—22no—
122C2×#214—22no—
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×C4⋊Dic3—21no—
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134#924—22no—
135#924—22no—
136C2×Dic3⋊C4—21no—
137C2×#208—22no—
138C2×#208—22no—
139C2×#208D414yescomplemented
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142D3×M16—232no—
143C2×ΓL(1,𝔽25)—22no—
144C2×ΓL(1,𝔽25)—22no—
145C2×ΓL(1,𝔽25)—22no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)—22no—
148C2×ΓL(1,𝔽25)D414yescomplemented
149C2×D3×C8—22no—
150C2×D3×C8—22no—
151C2×D3×C8—22no—
152C2×D3×C8—22no—
153C2×D3×C8—22no—
154C2×D3×C8D414yescomplemented
155#897—22no—
156#897—22no—
157#897—22no—
158#897—22no—
159C3×#102—22no—
160C3×#102—22no—
161C3×#95—21no—
162#832—22no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#816—22no—
169#816—22no—
170#810—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⋊Q8—31no—
188C2×#121—31no—
189C2×#121—31no—
190C2×#121C2×D311yescharacteristic
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×#103—31no—
200C2×#103—31no—
201C2×#102—31no—
202C2×#102C2×D311yescharacteristic, complemented
203C2×#102C2×D311yescharacteristic, complemented
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×C3—21no—
224C24×C3C2×D411yescharacteristic
225C23×D3—22no—
226C23×D3—22no—
227C23×D3—22no—
228C23×D3—22no—
229C23×D3—22no—
230C23×D3—41no—
231C23×D3—41no—
232C23×D3C2×D411yescharacteristic
233C23×D3C2×D411yescharacteristic
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D412yes—
252C22×C3×C4#4112yes—
253C22×C3×C4C2411yescharacteristic
254C2×#67—42no—
255C2×#67—42no—
256C2×#67—42no—
257C2×#67—42no—
258C2×#67—42no—
259C2×#67—42no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
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×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×C22⋊C4—42no—
311C3×C22⋊C4—42no—
312#217—42no—
313#217—42no—
314#217—42no—
315#217—42no—
316#214—44no—
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—
323C4⋊Dic3—21no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—42no—
330C4⋊Dic3—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×Q8—31no—
345C22×D4—21no—
346C22×D4—61no—
347C22×D4—61no—
348C22×D4C22×D311yescharacteristic
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—62no—
388C22⋊Q8—62no—
389C22⋊Q8—62no—
390C22⋊Q8—62no—
391C22⋊Q8—62no—
392C22⋊Q8—62no—
393#121—22no—
394#121—22no—
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—31no—
403C2×C4⋊C4—61no—
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—62no—
425#103—62no—
426#103—62no—
427#102—22no—
428#102—22no—
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—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3#12112yes—
450C23×C3C22×D411yescharacteristic
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—28no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—44no—
463C22×D3—44no—
464C22×D3—44no—
465C22×D3—44no—
466C22×D3—44no—
467C22×D3—44no—
468C22×D3#12112yes—
469C22×D3#12112yes—
470C22×D3AGL(1,ℤ/8)12yes—
471C22×D3#13712yes—
472C3×D4—41no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—41no—
476C3×D4—84no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
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#12112yes—
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499#67—84no—
500#67—84no—
501C2×Dic3—28no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—41no—
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—41no—
517C2×Dic3—41no—
518C2×Dic3#12112yes—
519C2×Dic3#12112yes—
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—22no—
536C3⋊C8—22no—
537C3⋊C8#12014yescomplemented
538C24—21no—
539C24—31no—
540C24—31no—
541C24—62no—
542C24—62no—
543C24—62no—
544C24—62no—
545C24—62no—
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—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
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—31no—
578C22×C4—31no—
579C22×C4—32no—
580C22×C4—32no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—68no—
588C22×C4—68no—
589C22×C4—68no—
590C22×C4—68no—
591C22×C4—62no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—61no—
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—61no—
638C4⋊C4—61no—
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×C3—81no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3C2×#12111yescharacteristic
673C22×C3C2×#12111yescharacteristic
674C22×C3C2×#12111yescharacteristic
675C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
676C22×C3C2×#13711yescharacteristic
677C22×C3#57511yescharacteristic
678C22×C3#57511yescharacteristic
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—416no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3#46814yescomplemented
694C3×C4—22no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—81no—
698C3×C4C2×#12011yescharacteristic
699C3×C4#52511yescharacteristic
700C3×C4#52511yescharacteristic
701C3×C4#52511yescharacteristic
702Dic3—22no—
703Dic3—22no—
704Dic3—81no—
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—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—68no—
726C23—61no—
727C23—61no—
728C23—61no—
729C23—61no—
730C23—61no—
731C23—61no—
732C23—61no—
733C23—61no—
734C23—61no—
735C23—61no—
736C23—124no—
737C23—124no—
738C23—124no—
739C23—124no—
740C23—124no—
741C23—124no—
742C23#88412yes—
743C23C2×D3×D411yescharacteristic
744Q8—121no—
745Q8—121no—
746Q8—121no—
747Q8—121no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—84no—
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—68no—
773C2×C4—68no—
774C2×C4—68no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
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—161no—
812C2×C3#284711yescharacteristic
813C2×C3C2×#46811yescharacteristic
814C2×C3#305411yescharacteristic
815C2×C3#305511yescharacteristic
816C2×C3#305511yescharacteristic
817C2×C3#305611yescharacteristic
818C2×C3#305611yescharacteristic
819D3—24no—
820D3—42no—
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—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—1216no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22C2×#88411yescharacteristic
851C22D3×#12111yescharacteristic
852C22D3×#12111yescharacteristic
853C22D3×AGL(1,ℤ/8)11yescharacteristic
854C22#577311yescharacteristic
855C22#577311yescharacteristic
856C22D3×#13711yescharacteristic
857C4—22no—
858C4—62no—
859C4—62no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—241no—
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—161no—
876C2#7493511yescharacteristic
877C2#7888911yescharacteristic
878C2#7893011yescharacteristic
879C2D3×#46811yescharacteristic
880C2#8080611yescharacteristic
881C2#8086311yescharacteristic
882C2#8086411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1895C2
socleC23×C3C22×D4
prime radical#82723C2
hypercenter#1895D3
hypocenterC3#32935
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
1. C22×D3×M16C2semidirect
3. C2×#5042C2semidirect
4. C2×#4780C2semidirect
5. C2×#4778C2semidirect
6. #74049C2semidirect
7. C3×#1895C2semidirect
8. #71989C2semidirect
9. #70203C2semidirect
10. #70202C2semidirect
11. #69513C2semidirect
12. #68884C2semidirect
13. #68882C2semidirect
14. #68870C2semidirect
15. #68869C2semidirect
23. C22×#214C22semidirect
35. C2×C3×#102C22semidirect
36. C2×C3×#102C22semidirect
39. C2×#832C22semidirect
41. C2×#816C22semidirect
42. C2×#816C22semidirect
48. C2×#810C22semidirect
49. C2×#808C22semidirect
50. C2×#807C22semidirect
51. C2×#807C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. #4551C22semidirect
63. #4551C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
73. #1895D3semidirect
139. C2×#208D4semidirect
148. C2×ΓL(1,𝔽25)D4semidirect
154. C2×D3×C8D4semidirect
202. C2×#102C2×D3semidirect
203. C2×#102C2×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
#827232
C2×#50422
C2×#47802
C2×#47782
#740492
C3×#18952
#719892
#702032
#702022
#695132
#688842
#688822
#688702
#688692
#329353