Finite Group Databasebeta

← #10830979

Subgroups — #10830979

Order 768.

1614 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#908C211yesmaximal, characteristic, complemented
2C2×#5127C211yesmaximal, characteristic, complemented
3C2×#4883C211yesmaximal, characteristic, complemented
4C2×#4864C211yesmaximal, characteristic, complemented
5#74016C211yesmaximal, characteristic, complemented
6#74015C211yesmaximal, characteristic, complemented
7C3×#1809C211yesmaximal, characteristic, complemented
8#70629C211yesmaximal, characteristic, complemented
9#70576C211yesmaximal, characteristic, complemented
10#69522C211yesmaximal, characteristic, complemented
11#69521C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68863C211yesmaximal, characteristic, complemented
15#68862C211yesmaximal, characteristic, complemented
16#24275—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C2×C4×#67C2211yescharacteristic
21C2×#908—24no—
22C2×#908—24no—
23C2×#908—24no—
24C22×D24C2211yescharacteristic
25C22×D24C2211yescharacteristic
26C22×#204C2211yescharacteristic
27C22×#204C2211yescharacteristic
28C22×D3×C8C2211yescharacteristic, complemented
29C2×#897C2211yescharacteristic, complemented
30C2×#895C2211yescharacteristic
31C2×#895C2211yescharacteristic
32C2×#895C2211yescharacteristic, complemented
33C2×#882—21no—
34C2×C3×#107C2211yescharacteristic, complemented
35C2×C3×#106C2211yescharacteristic, complemented
36C3×#380C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#830C2211yescharacteristic
39#5127—24no—
40C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
41C2×#815C2211yescharacteristic, complemented
42C2×Dic3⋊C8C2211yescharacteristic, complemented
43#4988C2211yescharacteristic
44#4988C2211yescharacteristic
45#4988C2211yescharacteristic, complemented
46#4973C2211yescharacteristic, complemented
47C2×#810C2211yescharacteristic, complemented
48C2×#810C2211yescharacteristic, complemented
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic, complemented
54C2×#809C2211yescharacteristic, complemented
55#4961—21no—
56#4960—21no—
57#4955—21no—
58#4883—24no—
59#4864—24no—
60#4672—21no—
61#4671—21no—
62#4668—21no—
63#4665—21no—
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)—31no—
67C2×#466—31no—
68C2×#465—31no—
69C2×#435—31no—
70#2408—31no—
71#2407—31no—
72#2055—31no—
73#2054—31no—
74#2000—31no—
75#1999—31no—
76#1973—31no—
77#1972—31no—
78#1809D311yescharacteristic, complemented
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—41no—
90C2×#235—41no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—21no—
96C22×D12—21no—
97C22×D12—21no—
98C22×D12—21no—
99C22×D12—41no—
100C22×D12—41no—
101C22×D12C2311yescharacteristic
102C22×D12C2311yescharacteristic
103C22×D12C2311yescharacteristic
104C22×C4×D3—21no—
105C22×C4×D3C2311yescharacteristic
106C22×Dic6C2311yescharacteristic
107C2×C3×M16—22no—
108C2×C3×M16—22no—
109C2×C3×M16D414yescomplemented
110C22×C3×C8C2311yescharacteristic
111C22×C3×C8C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×#217D411yescharacteristic
119C4×#67—22no—
120C4×#67—22no—
121C2×(C2×D3)⋊C4—21no—
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×(C2×D3)⋊C4D411yescharacteristic
132C2×C4⋊Dic3—21no—
133C2×Dic3⋊C4D411yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137#908—232no—
138C2×D24—22no—
139C2×D24—22no—
140C2×D24—22no—
141C2×D24—22no—
142C2×D24—22no—
143C2×D24D414yescomplemented
144C2×#204—22no—
145C2×#204—22no—
146C2×#204—22no—
147C2×#204—22no—
148C2×#204—22no—
149C2×#204D414yescomplemented
150C2×D3×C8—22no—
151C2×D3×C8—22no—
152C2×D3×C8—22no—
153#897—22no—
154#897—41no—
155#895—22no—
156#895—22no—
157#895—22no—
158#895—41no—
159#895—41no—
160#895—41no—
161#882—44no—
162C3×#107—22no—
163C3×#106—22no—
164C3×#95—21no—
165C3×#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#830—22no—
169(C2×D3)⋊C8—22no—
170#815—22no—
171Dic3⋊C8—22no—
172#810—22no—
173#810—41no—
174#809—22no—
175#809—22no—
176#809—22no—
177#809—41no—
178#809—41no—
179#809—41no—
180C22×#41—31no—
181C23×D4—31no—
182C2×AGL(1,ℤ/8)—64no—
183C2×AGL(1,ℤ/8)—64no—
184C2×AGL(1,ℤ/8)—64no—
185C22×SD16—31no—
186C22×SD16—31no—
187C22×D8—31no—
188C22×D8—31no—
189C22×M16C2×D311yescharacteristic
190C23×C8—31no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#120—61no—
196C2×C4×D4—31no—
197#466—64no—
198#465—64no—
199#435—64no—
200C2×#107C2×D311yescharacteristic, complemented
201C2×#106C2×D311yescharacteristic, complemented
202C2×C4⋊C8—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×#102—31no—
211C2×C22⋊C8—31no—
212C2×C22⋊C8—31no—
213C2×#97—31no—
214#394—61no—
215#394—61no—
216#392—61no—
217#392—61no—
218#391—31no—
219#390—31no—
220#390—31no—
221#390—31no—
222#386—61no—
223#385—61no—
224#380C2×D311yescharacteristic
225#380C2×D311yescharacteristic
226#379—61no—
227#340C2×D311yescharacteristic, complemented
228#340C2×D311yescharacteristic, complemented
229C24×C3C2×D411yescharacteristic
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—42no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—81no—
239C23×D3—81no—
240C23×D3C2×D411yescharacteristic
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×C4—21no—
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4#4112yes—
252C22×C3×C4C2411yescharacteristic
253C2×#67—22no—
254C2×#67—22no—
255C2×#67—41no—
256C2×#67—42no—
257C2×#67—42no—
258C2×#67—42no—
259C22×Dic3—21no—
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262C22×Dic3C2×D411yescharacteristic
263#235—28no—
264#235—44no—
265#235—44no—
266#235—44no—
267C2×D12—28no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—44no—
284C2×D12—44no—
285C2×D12—42no—
286C2×D12—42no—
287C2×D12—44no—
288C2×D12—42no—
289C2×D12—42no—
290C2×D12—42no—
291C2×D12—42no—
292C2×D12—42no—
293C2×D12—42no—
294C2×D12—42no—
295C2×D12—81no—
296C2×D12—81no—
297C2×D12—81no—
298C2×D12C2×D412yes—
299C2×D12C2×D412yes—
300C2×D12C2×D412yes—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—42no—
308C2×C4×D3—42no—
309C2×C4×D3—42no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6—21no—
314C2×Dic6—21no—
315C2×Dic6C2×D412yes—
316C3×M16—28no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8C2×D412yes—
320C2×C3×C8C2×D412yes—
321C2×C3×C8C2×D412yes—
322C2×C3×C8C2×D412yes—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C22⋊C4—42no—
332C3×C22⋊C4—81no—
333#217—22no—
334(C2×D3)⋊C4—22no—
335(C2×D3)⋊C4—42no—
336(C2×D3)⋊C4—42no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—42no—
341(C2×D3)⋊C4—42no—
342(C2×D3)⋊C4—81no—
343(C2×D3)⋊C4—81no—
344(C2×D3)⋊C4—81no—
345C4⋊Dic3—42no—
346Dic3⋊C4—22no—
347C4×Dic3—21no—
348C4×Dic3—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355D24—28no—
356D24—28no—
357#204—28no—
358#204—28no—
359D3×C8—44no—
360C25—61no—
361C2×#41—62no—
362C2×#41—62no—
363C2×#41—62no—
364C2×#41—62no—
365C2×#41—121no—
366C2×#41—121no—
367C22×Q8—31no—
368C22×D4—31no—
369C22×D4—31no—
370C22×D4—31no—
371C22×D4—31no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—61no—
375C22×D4—61no—
376C22×D4—61no—
377C22×D4—61no—
378C22×D4—62no—
379C22×D4—61no—
380C22×D4—62no—
381C22×D4—121no—
382C22×D4—121no—
383C23×C4—31no—
384C23×C4—61no—
385C23×C4C22×D311yescharacteristic
386AGL(1,ℤ/8)—632no—
387C2×SD16—34no—
388C2×SD16—62no—
389C2×SD16—62no—
390C2×SD16—62no—
391C2×SD16—62no—
392C2×SD16—62no—
393C2×D8—34no—
394C2×D8—62no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×M16—22no—
400C2×M16—22no—
401C2×M16D1214yescomplemented
402C22×C8—31no—
403C22×C8—31no—
404C22×C8—62no—
405C22×C8—62no—
406C22×C8—62no—
407C22×C8C22×D311yescharacteristic
408C22×C8C22×D311yescharacteristic
409C22⋊Q8—62no—
410C22⋊Q8—121no—
411#121—62no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
416#121—121no—
417#120—124no—
418C4×D4—62no—
419C4×D4—62no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C4⋊C4C22×D311yescharacteristic
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C4⋊C4C22×D311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—31no—
429C2×C22⋊C4—31no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C42—31no—
441#107—22no—
442#106—22no—
443C4⋊C8—62no—
444#103—62no—
445#103—121no—
446#102—62no—
447#102—62no—
448#102—62no—
449#102—121no—
450#102—121no—
451#102—121no—
452C22⋊C8—62no—
453C22⋊C8—62no—
454#97—62no—
455#95—21no—
456#95—21no—
457#95—61no—
458#95—61no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3#12112yes—
466C23×C3C22×D411yescharacteristic
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—48no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—84no—
496C22×D3—84no—
497C22×D3—84no—
498C22×D3—84no—
499C22×D3—84no—
500C22×D3—84no—
501C22×D3AGL(1,ℤ/8)12yescomplemented
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4#12112yes—
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4C22×D411yescharacteristic
523C2×C3×C4C22×D411yescharacteristic
524C2×C3×C4C2×#4111yescharacteristic
525C2×C3×C4H(5,𝔽2)11yescharacteristic
526C2×C3×C4H(5,𝔽2)11yescharacteristic
527#67—44no—
528#67—48no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—22no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541D12—22no—
542D12—22no—
543D12—22no—
544D12—22no—
545D12—22no—
546D12—22no—
547D12—48no—
548D12—41no—
549D12—41no—
550D12—41no—
551D12—41no—
552D12—41no—
553D12—41no—
554D12—84no—
555D12—84no—
556D12—84no—
557C4×D3—48no—
558C4×D3—41no—
559C4×D3—41no—
560C4×D3—41no—
561C4×D3—41no—
562Dic6—22no—
563Dic6—22no—
564Dic6—41no—
565Dic6—41no—
566C3×C8—22no—
567C3×C8#12014yescomplemented
568C3⋊C8—41no—
569C3⋊C8—41no—
570C24—31no—
571C24—61no—
572C24—61no—
573C24—61no—
574C24—122no—
575C24—122no—
576C24—122no—
577C24—122no—
578C24—122no—
579C24—241no—
580C24—241no—
581C24D3×D411yescharacteristic
582#41—68no—
583#41—124no—
584#41—124no—
585#41—124no—
586C2×Q8—32no—
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8—61no—
591C2×Q8—61no—
592C2×D4—32no—
593C2×D4—32no—
594C2×D4—32no—
595C2×D4—68no—
596C2×D4—62no—
597C2×D4—62no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—122no—
616C2×D4—122no—
617C2×D4—124no—
618C2×D4—122no—
619C2×D4—122no—
620C2×D4—122no—
621C2×D4—122no—
622C2×D4—122no—
623C2×D4—122no—
624C2×D4—121no—
625C2×D4—122no—
626C2×D4—122no—
627C2×D4—122no—
628C2×D4—122no—
629C2×D4—241no—
630C2×D4—241no—
631C2×D4—241no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—122no—
651C22×C4—122no—
652C22×C4—122no—
653C22×C4C2×D1212yes—
654C22×C4D3×D411yescharacteristic
655C22×C4#23912yes—
656C22×C4C23×D311yescharacteristic
657SD16—68no—
658SD16—68no—
659D8—68no—
660D8—68no—
661M16—28no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—61no—
665C2×C8—61no—
666C2×C8—61no—
667C2×C8—61no—
668C2×C8—61no—
669C2×C8—61no—
670C2×C8—124no—
671C2×C8C2×D1212yes—
672C2×C8C2×D1212yes—
673C2×C8D3×D412yes—
674C2×C8D3×D412yes—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—62no—
684C4⋊C4—122no—
685C22⋊C4—42no—
686C22⋊C4—62no—
687C22⋊C4—62no—
688C22⋊C4—81no—
689C22⋊C4—122no—
690C22⋊C4—122no—
691C22⋊C4—122no—
692C22⋊C4—122no—
693C22⋊C4—122no—
694C22⋊C4—122no—
695C22⋊C4—122no—
696C22⋊C4—241no—
697C22⋊C4—241no—
698C22⋊C4—241no—
699C42—61no—
700C42—61no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3C2×#12111yescharacteristic
709C22×C3D4211yescharacteristic
710C22×C3D4211yescharacteristic
711C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
712C22×C3#57511yescharacteristic
713C22×C3#57611yescharacteristic
714C22×C3#57711yescharacteristic
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—42no—
726C2×D3—42no—
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—816no—
732C2×D3—81no—
733C2×D3—81no—
734C2×D3—81no—
735C2×D3—81no—
736C2×D3—81no—
737C2×D3—81no—
738C2×D3—81no—
739C2×D3—81no—
740C2×D3—81no—
741C2×D3—81no—
742C2×D3—81no—
743C2×D3—81no—
744C3×C4—22no—
745C3×C4—81no—
746C3×C4—81no—
747C3×C4—81no—
748C3×C4—81no—
749C3×C4C2×#12011yescharacteristic
750C3×C4#53511yescharacteristic
751C3×C4#54611yescharacteristic
752C3×C4#54611yescharacteristic
753Dic3—42no—
754Dic3—41no—
755Dic3—41no—
756Dic3—41no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—32no—
764C23—61no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23—62no—
771C23—62no—
772C23—62no—
773C23—128no—
774C23—121no—
775C23—121no—
776C23—121no—
777C23—121no—
778C23—121no—
779C23—121no—
780C23—121no—
781C23—121no—
782C23—121no—
783C23—121no—
784C23—121no—
785C23—121no—
786C23—121no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—244no—
793C23—244no—
794C23—244no—
795C23—244no—
796C23—244no—
797C23—244no—
798C23#89512yes—
799C23C2×D3×D411yescharacteristic
800Q8—62no—
801Q8—62no—
802Q8—121no—
803Q8—121no—
804D4—62no—
805D4—62no—
806D4—62no—
807D4—62no—
808D4—62no—
809D4—62no—
810D4—128no—
811D4—124no—
812D4—128no—
813D4—121no—
814D4—121no—
815D4—121no—
816D4—121no—
817D4—121no—
818D4—121no—
819D4—244no—
820D4—244no—
821D4—244no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—62no—
850C2×C4—128no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4#89512yes—
858C2×C4C22×D1211yescharacteristic
859C2×C4C2×D3×D411yescharacteristic
860C2×C4C2×D3×D411yescharacteristic
861C2×C4C2×#23911yescharacteristic
862C2×C4#100911yescharacteristic
863C2×C4#100911yescharacteristic
864C8—22no—
865C8—121no—
866C8—121no—
867C8#88214yescomplemented
868C2×C3—42no—
869C2×C3#240811yescharacteristic
870C2×C3#305511yescharacteristic
871C2×C3#306211yescharacteristic
872C2×C3#326411yescharacteristic
873C2×C3#326511yescharacteristic
874C2×C3#326711yescharacteristic
875C2×C3#326811yescharacteristic
876D3—42no—
877D3—82no—
878D3—82no—
879D3—82no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—62no—
888C22—62no—
889C22—62no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—122no—
895C22—122no—
896C22—122no—
897C22—122no—
898C22—122no—
899C22—122no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22—2416no—
904C22—241no—
905C22—241no—
906C22—241no—
907C22—241no—
908C22—241no—
909C22—241no—
910C22—241no—
911C22—241no—
912C22—241no—
913C22—241no—
914C22—241no—
915C22—241no—
916C22C2×#89511yescharacteristic
917C22#560911yescharacteristic
918C22#560911yescharacteristic
919C22D3×AGL(1,ℤ/8)11yescharacteristic
920C22#577411yescharacteristic
921C22#577711yescharacteristic
922C22#577811yescharacteristic
923C4—22no—
924C4—81no—
925C4—81no—
926C4—81no—
927C4—81no—
928C4—121no—
929C4—122no—
930C4—121no—
931C4—121no—
932C4C2×#88211yescharacteristic
933C4#552511yescharacteristic
934C4#563011yescharacteristic
935C4#563011yescharacteristic
936C3#2427511yescharacteristic, complemented, Sylow
937C2—42no—
938C2—122no—
939C2—242no—
940C2—242no—
941C2—242no—
942C2#7401611yescharacteristic
943C2#7921111yescharacteristic
944C2#7921311yescharacteristic
945C2#8083411yescharacteristic
946C2#8083611yescharacteristic
947C2#8088111yescharacteristic
948C2#8092111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1809C2
socleC23×C3C22×D4
hypercenter#1809D3
hypocenterC3#24275
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×#908C2semidirect
2. C2×#5127C2semidirect
3. C2×#4883C2semidirect
4. C2×#4864C2semidirect
5. #74016C2semidirect
6. #74015C2semidirect
7. C3×#1809C2semidirect
8. #70629C2semidirect
9. #70576C2semidirect
10. #69522C2semidirect
11. #69521C2semidirect
12. #68887C2semidirect
13. #68886C2semidirect
14. #68863C2semidirect
15. #68862C2semidirect
28. C22×D3×C8C22semidirect
29. C2×#897C22semidirect
32. C2×#895C22semidirect
34. C2×C3×#107C22semidirect
35. C2×C3×#106C22semidirect
40. C2×(C2×D3)⋊C8C22semidirect
41. C2×#815C22semidirect
42. C2×Dic3⋊C8C22semidirect
45. #4988C22semidirect
46. #4973C22semidirect
47. C2×#810C22semidirect
48. C2×#810C22semidirect
53. C2×#809C22semidirect
54. C2×#809C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
78. #1809D3semidirect
109. C2×C3×M16D4semidirect
143. C2×D24D4semidirect
149. C2×#204D4semidirect
200. C2×#107C2×D3semidirect
201. C2×#106C2×D3semidirect
227. #340C2×D3semidirect
228. #340C2×D3semidirect
401. C2×M16D12semidirect
501. C22×D3AGL(1,ℤ/8)semidirect
567. C3×C8#120semidirect
867. C8#882semidirect
936. C3#24275semidirect

Maximal subgroups

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

subgroupindex
C22×#9082
C2×#51272
C2×#48832
C2×#48642
#740162
#740152
C3×#18092
#706292
#705762
#695222
#695212
#688872
#688862
#688632
#688622
#242753