Finite Group Databasebeta

← #10831005

Subgroups — #10831005

Order 768.

1608 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×#914C211yesmaximal, characteristic, complemented
2C2×#5174C211yesmaximal, characteristic, complemented
3C2×#4865C211yesmaximal, characteristic, complemented
4C2×#4688C211yesmaximal, characteristic, complemented
5#76618C211yesmaximal, characteristic, complemented
6#76436C211yesmaximal, characteristic, complemented
7C3×#1968C211yesmaximal, characteristic, complemented
8#70578C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70267C211yesmaximal, characteristic, complemented
11#70204C211yesmaximal, characteristic, complemented
12#70198C211yesmaximal, characteristic, complemented
13#69776C211yesmaximal, characteristic, complemented
14#69680C211yesmaximal, characteristic, complemented
15#69650C211yesmaximal, characteristic, complemented
16#24277—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×#946C2211yescharacteristic, complemented
21C22×#215C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#914—24no—
25C2×#914—24no—
26C2×#914—24no—
27C22×D24C2211yescharacteristic
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30C2×#895C2211yescharacteristic
31C2×#895C2211yescharacteristic, complemented
32C2×#882—21no—
33C2×C4×D12C2211yescharacteristic
34C2×C3×#106C2211yescharacteristic, complemented
35C2×C3×#103C2211yescharacteristic, complemented
36C2×C3×#102C2211yescharacteristic
37C2×C3×C4×C8C2211yescharacteristic, complemented
38C3×#391C2211yescharacteristic, complemented
39C3×#390C2211yescharacteristic
40C2×#835C2211yescharacteristic, complemented
41C2×#832C2211yescharacteristic
42#5174—24no—
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic, complemented
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
47C2×#818C2211yescharacteristic, complemented
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic, complemented
52#4961—21no—
53#4960—21no—
54#4955—21no—
55#4939C2211yescharacteristic
56#4939C2211yescharacteristic, complemented
57C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
58#4865—24no—
59#4688—24no—
60#4672—21no—
61#4671—21no—
62#4668—21no—
63#4665—21no—
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)—31no—
67C2×#469—31no—
68C2×#468—31no—
69C2×#436—31no—
70#2408—31no—
71#2407—31no—
72#2055—31no—
73#2054—31no—
74#2000—31no—
75#1999—31no—
76#1970—31no—
77#1968D311yescharacteristic, complemented
78#1809—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—41no—
91C2×#239—41no—
92C2×D3×D4—22no—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—41no—
97C2×D3×D4—41no—
98C22×D12—21no—
99C22×D12—21no—
100C22×D12—21no—
101C22×D12D411yescharacteristic
102C22×D12C2311yescharacteristic
103C22×D12C2311yescharacteristic
104C22×C4×D3—21no—
105C22×C4×D3C2311yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C2×C3×SD16—22no—
108C2×C3×SD16—22no—
109C2×C3×SD16D414yescomplemented
110C22×C3×C8C2311yescharacteristic
111C22×C3×C8C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C42C2311yescharacteristic
117C2×#217—21no—
118#946—22no—
119#946—41no—
120C2×#215—22no—
121C2×#215—22no—
122C2×#215—22no—
123#938—22no—
124#938—41no—
125C2×#213—22no—
126C2×#213—22no—
127C2×#213—22no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4D411yescharacteristic
138C2×(C2×D3)⋊C4D411yescharacteristic
139C2×C4⋊Dic3D411yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×Dic3⋊C4—21no—
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145#914—232no—
146C2×D24—22no—
147C2×D24—22no—
148C2×D24D414yescomplemented
149C2×ΓL(1,𝔽25)—22no—
150C2×ΓL(1,𝔽25)—22no—
151C2×ΓL(1,𝔽25)—22no—
152C2×ΓL(1,𝔽25)—22no—
153C2×ΓL(1,𝔽25)—22no—
154C2×ΓL(1,𝔽25)D414yescomplemented
155#895—22no—
156#895—22no—
157#895—41no—
158#895—41no—
159#882—44no—
160C4×D12—22no—
161C4×D12—22no—
162C3×#106—22no—
163C3×#103—41no—
164C3×#102—41no—
165C3×C4×C8—22no—
166C3×#95—21no—
167C3×#95—21no—
168#835—22no—
169#832—22no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172#821—41no—
173#821—41no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—22no—
176#818—22no—
177#809—22no—
178#809—22no—
179C4⋊(C3⋊C8)—22no—
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×SD16C2×D311yescharacteristic
187C22×D8—31no—
188C22×D8—31no—
189C22×M16—31no—
190C22×M16—31no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#120—61no—
196C2×C4×D4—31no—
197#469—64no—
198#468—64no—
199#436—64no—
200C2×#107—31no—
201C2×#106C2×D311yescharacteristic, complemented
202C2×C4⋊C8—31no—
203C2×#103—31no—
204C2×#103C2×D311yescharacteristic, complemented
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×#102C2×D311yescharacteristic
211C2×C22⋊C8—31no—
212C2×C22⋊C8—31no—
213C2×C4×C8C2×D311yescharacteristic, complemented
214#394—61no—
215#394—61no—
216#392—61no—
217#392—61no—
218#391C2×D311yescharacteristic, complemented
219#390—31no—
220#390—31no—
221#390C2×D311yescharacteristic
222#386—61no—
223#385—61no—
224#380—31no—
225#380—31no—
226#379—61no—
227#340—31no—
228#340—31no—
229C24×C3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—42no—
233C23×D3—42no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—81no—
238C23×D3—81no—
239C23×D3C2×D411yescharacteristic
240C23×D3C2×D411yescharacteristic
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8C2×D412yes—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4C2×D412yes—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—81no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269#239—28no—
270#239—44no—
271#239—44no—
272#239—44no—
273D3×D4—28no—
274D3×D4—44no—
275D3×D4—44no—
276D3×D4—44no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—22no—
286C2×D12—22no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—41no—
290C2×D12—42no—
291C2×D12—42no—
292C2×D12—42no—
293C2×D12—42no—
294C2×D12—42no—
295C2×D12—42no—
296C2×D12—42no—
297C2×D12—81no—
298C2×D12—81no—
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—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—42no—
312C2×C4×D3—42no—
313C2×C4×D3—42no—
314C2×C4×D3C2×D412yes—
315C2×C4×D3#4112yes—
316C3×SD16—28no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
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×C22⋊C4—42no—
328C3×C22⋊C4—81no—
329C3×C42—21no—
330C3×C42—21no—
331#217—42no—
332#215—28no—
333#213—28no—
334(C2×D3)⋊C4—22no—
335(C2×D3)⋊C4—22no—
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—22no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350Dic3⋊C4—42no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8C2×D412yes—
357D24—28no—
358ΓL(1,𝔽25)—28no—
359ΓL(1,𝔽25)—44no—
360C25—61no—
361C2×#41—62no—
362C2×#41—62no—
363C2×#41—62no—
364C2×#41—62no—
365C2×#41—121no—
366C2×#41—121no—
367C22×Q8C22×D311yescharacteristic
368C22×D4—31no—
369C22×D4—31no—
370C22×D4—31no—
371C22×D4—61no—
372C22×D4—61no—
373C22×D4—61no—
374C22×D4—62no—
375C22×D4—62no—
376C22×D4—61no—
377C22×D4—62no—
378C22×D4—62no—
379C22×D4—61no—
380C22×D4—121no—
381C22×D4—121no—
382C22×D4C22×D311yescharacteristic
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—61no—
386AGL(1,ℤ/8)—632no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—62no—
390C2×SD16—62no—
391C2×SD16—62no—
392C2×SD16D1214yescomplemented
393C2×D8—34no—
394C2×D8—62no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×M16—34no—
400C2×M16—62no—
401C2×M16—62no—
402C2×M16—62no—
403C2×M16—62no—
404C2×M16—62no—
405C22×C8—31no—
406C22×C8—31no—
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—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—61no—
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×C42C22×D311yescharacteristic
441#107—62no—
442#106—22no—
443C4⋊C8—62no—
444#103—41no—
445#103—62no—
446#102—41no—
447#102—62no—
448#102—62no—
449#102—62no—
450#102—121no—
451#102—121no—
452C22⋊C8—62no—
453C22⋊C8—62no—
454C4×C8—22no—
455#95—21no—
456#95—21no—
457#95—61no—
458#95—61no—
459C23×C3—22no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3C22×D411yescharacteristic
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—48no—
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×D3#12112yes—
502C3×Q8—22no—
503C3×Q8—22no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—41no—
509C3×D4—41no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4AGL(1,ℤ/8)12yescomplemented
525C2×C3×C4C22×D411yescharacteristic
526C2×C3×C4C22×D411yescharacteristic
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C2×#4111yescharacteristic
529C2×C3×C4H(5,𝔽2)11yescharacteristic
530C2×C3×C4H(5,𝔽2)11yescharacteristic
531#67—48no—
532#67—84no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3#12112yes—
545D12—22no—
546D12—22no—
547D12—22no—
548D12—22no—
549D12—44no—
550D12—48no—
551D12—41no—
552D12—41no—
553D12—41no—
554D12—41no—
555D12—84no—
556D12—84no—
557C4×D3—22no—
558C4×D3—22no—
559C4×D3—22no—
560C4×D3—22no—
561C4×D3—48no—
562C4×D3—41no—
563C4×D3—41no—
564C4×D3—41no—
565C4×D3—41no—
566C3×C8—41no—
567C3×C8#12014yescomplemented
568C3⋊C8—22no—
569C3⋊C8—41no—
570C24—21no—
571C24—31no—
572C24—31no—
573C24—61no—
574C24—61no—
575C24—122no—
576C24—122no—
577C24—122no—
578C24—122no—
579C24—122no—
580C24—241no—
581C24—241no—
582#41—68no—
583#41—124no—
584#41—124no—
585#41—124no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8C2×D1212yes—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—32no—
598C2×D4—32no—
599C2×D4—62no—
600C2×D4—68no—
601C2×D4—62no—
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—121no—
613C2×D4—122no—
614C2×D4—122no—
615C2×D4—122no—
616C2×D4—122no—
617C2×D4—122no—
618C2×D4—122no—
619C2×D4—122no—
620C2×D4—122no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—122no—
627C2×D4—122no—
628C2×D4—241no—
629C2×D4—241no—
630C2×D4—241no—
631C2×D4C2×D1212yes—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—31no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—31no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—122no—
652C22×C4—122no—
653C22×C4—122no—
654C22×C4D3×D411yescharacteristic
655C22×C4D3×D411yescharacteristic
656C22×C4C23×D311yescharacteristic
657SD16—28no—
658SD16—68no—
659D8—68no—
660D8—68no—
661M16—68no—
662M16—124no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—32no—
667C2×C8—61no—
668C2×C8—61no—
669C2×C8—61no—
670C2×C8—61no—
671C2×C8—61no—
672C2×C8C2×D1212yes—
673C2×C8D3×D412yes—
674C2×C8D3×D412yes—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—62no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
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—21no—
700C42—21no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
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—41no—
724C2×D3—42no—
725C2×D3—41no—
726C2×D3—42no—
727C2×D3—42no—
728C2×D3—41no—
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—816no—
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—42no—
746C3×C4—41no—
747C3×C4—81no—
748C3×C4—81no—
749C3×C4C2×#12011yescharacteristic
750C3×C4#53511yescharacteristic
751C3×C4#54611yescharacteristic
752C3×C4#54611yescharacteristic
753Dic3—22no—
754Dic3—41no—
755Dic3—81no—
756Dic3—81no—
757C23—22no—
758C23—32no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23—61no—
771C23—62no—
772C23—62no—
773C23—61no—
774C23—61no—
775C23—61no—
776C23—61no—
777C23—61no—
778C23—61no—
779C23—61no—
780C23—128no—
781C23—121no—
782C23—121no—
783C23—121no—
784C23—121no—
785C23—121no—
786C23—121no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—121no—
793C23—244no—
794C23—244no—
795C23—244no—
796C23—244no—
797C23—244no—
798C23—244no—
799C23C2×D3×D411yescharacteristic
800Q8—22no—
801Q8—22no—
802Q8—41no—
803Q8—41no—
804D4—22no—
805D4—22no—
806D4—41no—
807D4—41no—
808D4—62no—
809D4—62no—
810D4—62no—
811D4—62no—
812D4—124no—
813D4—128no—
814D4—128no—
815D4—121no—
816D4—121no—
817D4—121no—
818D4—121no—
819D4—244no—
820D4—244no—
821D4—244no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—32no—
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—61no—
838C2×C4—61no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—128no—
847C2×C4—121no—
848C2×C4—121no—
849C2×C4—121no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4#91412yescomplemented
858C2×C4C22×D1211yescharacteristic
859C2×C4C2×D3×D411yescharacteristic
860C2×C4C2×D3×D411yescharacteristic
861C2×C4#100411yescharacteristic
862C2×C4D3×#4111yescharacteristic
863C2×C4#100911yescharacteristic
864C8—41no—
865C8—62no—
866C8—121no—
867C8#88214yescomplemented
868C2×C3—82no—
869C2×C3#240811yescharacteristic
870C2×C3#305511yescharacteristic
871C2×C3#306211yescharacteristic
872C2×C3#327211yescharacteristic
873C2×C3#327311yescharacteristic
874C2×C3#327411yescharacteristic
875C2×C3#327511yescharacteristic
876D3—42no—
877D3—81no—
878D3—82no—
879D3—82no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—62no—
884C22—62no—
885C22—62no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—122no—
900C22—122no—
901C22—122no—
902C22—121no—
903C22—122no—
904C22—121no—
905C22—122no—
906C22—122no—
907C22—2416no—
908C22—241no—
909C22—241no—
910C22—241no—
911C22—241no—
912C22—241no—
913C22—241no—
914C22—241no—
915C22—241no—
916C22D4×D1211yescharacteristic
917C22D3×#12111yescharacteristic
918C22#571711yescharacteristic
919C22C2×#91411yescharacteristic
920C22#576211yescharacteristic
921C22#576811yescharacteristic
922C22#576911yescharacteristic
923C4—22no—
924C4—41no—
925C4—42no—
926C4—62no—
927C4—81no—
928C4—81no—
929C4—121no—
930C4—241no—
931C4—241no—
932C4C2×#88211yescharacteristic
933C4#555411yescharacteristic
934C4#560711yescharacteristic
935C4#567611yescharacteristic
936C3#2427711yescharacteristic, complemented, Sylow
937C2—82no—
938C2—122no—
939C2—241no—
940C2—242no—
941C2—242no—
942C2#7643611yescharacteristic
943C2#7967011yescharacteristic
944C2#7967111yescharacteristic
945C2#8065711yescharacteristic
946C2#8066111yescharacteristic
947C2#8177011yescharacteristic
948C2#8182911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1968C2
socleC23×C3C22×D4
hypercenter#1968D3
hypocenterC3#24277
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
1. C22×#914C2semidirect
2. C2×#5174C2semidirect
3. C2×#4865C2semidirect
4. C2×#4688C2semidirect
5. #76618C2semidirect
6. #76436C2semidirect
7. C3×#1968C2semidirect
8. #70578C2semidirect
9. #70272C2semidirect
10. #70267C2semidirect
11. #70204C2semidirect
12. #70198C2semidirect
13. #69776C2semidirect
14. #69680C2semidirect
15. #69650C2semidirect
20. C2×#946C22semidirect
29. C22×ΓL(1,𝔽25)C22semidirect
31. C2×#895C22semidirect
34. C2×C3×#106C22semidirect
35. C2×C3×#103C22semidirect
37. C2×C3×C4×C8C22semidirect
38. C3×#391C22semidirect
40. C2×#835C22semidirect
44. C2×#821C22semidirect
46. C2×(C2×D3)⋊C8C22semidirect
47. C2×#818C22semidirect
51. C2×#809C22semidirect
56. #4939C22semidirect
57. C2×C4⋊(C3⋊C8)C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
77. #1968D3semidirect
109. C2×C3×SD16D4semidirect
148. C2×D24D4semidirect
154. C2×ΓL(1,𝔽25)D4semidirect
201. C2×#106C2×D3semidirect
204. C2×#103C2×D3semidirect
213. C2×C4×C8C2×D3semidirect
218. #391C2×D3semidirect
392. C2×SD16D12semidirect
524. C2×C3×C4AGL(1,ℤ/8)semidirect
567. C3×C8#120semidirect
857. C2×C4#914semidirect
867. C8#882semidirect
936. C3#24277semidirect

Maximal subgroups

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

subgroupindex
C22×#9142
C2×#51742
C2×#48652
C2×#46882
#766182
#764362
C3×#19682
#705782
#702722
#702672
#702042
#701982
#697762
#696802
#696502
#242773