Finite Group Databasebeta

← #10827339

Subgroups — #10827339

Order 768.

1690 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5726C211yesmaximal, characteristic, complemented
2C2×#4773C211yesmaximal, characteristic, complemented
3C2×D3×#102C211yesmaximal, characteristic, complemented
4#76436C211yesmaximal, characteristic, complemented
5C3×#2023C211yesmaximal, characteristic, complemented
6#71792C211yesmaximal, characteristic, complemented
7#70204C211yesmaximal, characteristic, complemented
8#70200C211yesmaximal, characteristic, complemented
9#69657C211yesmaximal, characteristic, complemented
10#68886C211yesmaximal, characteristic, complemented
11#68883C211yesmaximal, characteristic, complemented
12#68880C211yesmaximal, characteristic, complemented
13#68871C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68668C211yesmaximal, characteristic, complemented
16#23960—31nomaximal, Sylow
17C22×#239—21no—
18C22×D3×D4C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic, complemented
20C2×#946—21no—
21C2×#938C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C22×D24C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25#5726—24no—
26#5726—24no—
27C2×#895C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#895C2211yescharacteristic, complemented
30C2×#894—21no—
31C2×#894—21no—
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×D3×C4⋊C4C2211yescharacteristic, complemented
34C2×#882—21no—
35C2×C4×D12C2211yescharacteristic
36C2×C4×D12C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic, complemented
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
45C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
46#4987C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic, complemented
50#4961—21no—
51#4960—21no—
52#4955—21no—
53#4939C2211yescharacteristic
54#4773—24no—
55D3×#102—24no—
56C3×#340C2211yescharacteristic, complemented
57C3×#340C2211yescharacteristic, complemented
58C3×#336C2211yescharacteristic, complemented
59#4551C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4524C2211yescharacteristic, complemented
64C2×#547—31no—
65C2×#447—31no—
66C22×#102—31no—
67#2408—31no—
68#2023—31no—
69#2023D311yescharacteristic, complemented
70#1999—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1879—31no—
75#1874—31no—
76#1874—31no—
77#1869—31no—
78#1823—31no—
79C24×D3—21no—
80C22×C3×Q8—21no—
81C22×C3×D4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C2×#239—28no—
85C2×#239—44no—
86C2×#239—44no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—41no—
92C2×D3×D4—41no—
93C22×D12—21no—
94C22×D12—21no—
95C22×D12—21no—
96C22×D12D411yescharacteristic
97C22×D12C2311yescharacteristic
98C22×D12C2311yescharacteristic
99C22×C4×D3—21no—
100C22×C4×D3—21no—
101C22×C4×D3—21no—
102C22×C4×D3C2311yescharacteristic
103C22×C4×D3C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×C4⋊Q8—22no—
107C3×C4⋊Q8—22no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C42C2311yescharacteristic
115C2×#217—21no—
116#946—28no—
117#938—22no—
118#938—41no—
119C2×#213—22no—
120C2×#213—22no—
121C2×#213—41no—
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)⋊C4D411yescharacteristic
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×C4⋊Dic3D411yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C2×D24—22no—
139C2×D24—22no—
140C2×D24—41no—
141C2×D3×C8—22no—
142C2×D3×C8—41no—
143C2×D3×C8—41no—
144#895—22no—
145#895—22no—
146#895—22no—
147#895—22no—
148#895—41no—
149#895D414yescomplemented
150#894—28no—
151#894—28no—
152D3×C4⋊C4—22no—
153D3×C4⋊C4—22no—
154D3×C4⋊C4—22no—
155D3×C4⋊C4D414yescomplemented
156#882—44no—
157C4×D12—22no—
158C4×D12—22no—
159C4×D12—22no—
160C4×D12—22no—
161C3×#102—22no—
162C3×#102—22no—
163#832—22no—
164C3⋊#95—21no—
165#821—22no—
166#821—41no—
167(C2×D3)⋊C8—22no—
168(C2×D3)⋊C8—41no—
169(C2×D3)⋊C8—41no—
170#809—22no—
171#809—22no—
172#809—41no—
173C22×#41—61no—
174C23×D4—31no—
175C22×D8—31no—
176C22×D8—31no—
177C23×C8—31no—
178#547—64no—
179#547—64no—
180C2×C4⋊Q8C2×D311yescharacteristic, complemented
181C2×#123—61no—
182C2×#123—61no—
183C2×C22⋊Q8—61no—
184C2×#121—31no—
185C2×#121—31no—
186C2×#121—31no—
187C2×#121—31no—
188C2×#120—61no—
189C2×C4×D4—31no—
190C2×C4×D4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193#447—64no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×#102—64no—
201C2×#102C2×D311yescharacteristic
202C2×#102C2×D311yescharacteristic
203C2×C22⋊C8—31no—
204C2×C22⋊C8—31no—
205C2×C22⋊C8—31no—
206#394—61no—
207#392—61no—
208#390—31no—
209#390C2×D311yescharacteristic
210#380—31no—
211#379—61no—
212#340—31no—
213#340—31no—
214#340—31no—
215#340—31no—
216#340C2×D311yescharacteristic, complemented
217#340C2×D311yescharacteristic, complemented
218#336—31no—
219#336C2×D311yescharacteristic, complemented
220C24×C3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—42no—
224C23×D3—42no—
225C23×D3—42no—
226C23×D3—42no—
227C23×D3—42no—
228C23×D3—81no—
229C23×D3—81no—
230C23×D3C2×D411yescharacteristic
231C23×D3C2×D411yescharacteristic
232C2×C3×Q8—24no—
233C2×C3×Q8—42no—
234C2×C3×Q8—42no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4#4112yescomplemented
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—81no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3C2×D411yescharacteristic
256C22×Dic3C2×D411yescharacteristic
257#239—432no—
258D3×D4—28no—
259D3×D4—44no—
260D3×D4—44no—
261D3×D4—44no—
262C2×D12—22no—
263C2×D12—22no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—24no—
273C2×D12—24no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—42no—
277C2×D12—42no—
278C2×D12—42no—
279C2×D12—42no—
280C2×D12—42no—
281C2×D12—42no—
282C2×D12—81no—
283C2×D12D814yescomplemented
284C2×D12C2×D412yes—
285C2×D12#4112yescomplemented
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—24no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C2×C4×D3—42no—
304C2×C4×D3—42no—
305C2×C4×D3C2×D412yes—
306C2×C4×D3C2×D412yes—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C3×C4⋊C4—24no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4C2×D412yes—
319C3×C4⋊C4C2×D412yes—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—81no—
322C3×C42—21no—
323C3×C42—21no—
324#217—42no—
325#213—44no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—22no—
329(C2×D3)⋊C4—22no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—42no—
332(C2×D3)⋊C4—42no—
333(C2×D3)⋊C4—42no—
334(C2×D3)⋊C4—81no—
335C4⋊Dic3—21no—
336C4⋊Dic3—22no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3C2×D412yes—
340Dic3⋊C4—24no—
341Dic3⋊C4—24no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348D24—44no—
349D3×C8—44no—
350C25—61no—
351C2×#41—68no—
352C2×#41—124no—
353C2×#41—124no—
354C22×Q8—21no—
355C22×D4—31no—
356C22×D4—31no—
357C22×D4—31no—
358C22×D4—61no—
359C22×D4—61no—
360C22×D4—61no—
361C22×D4—62no—
362C22×D4—62no—
363C22×D4—61no—
364C22×D4—62no—
365C22×D4—62no—
366C22×D4—61no—
367C22×D4—121no—
368C22×D4—121no—
369C22×D4C22×D311yescharacteristic
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—61no—
373C23×C4—61no—
374C23×C4—61no—
375C2×D8—62no—
376C2×D8—62no—
377C2×D8—62no—
378C2×D8—62no—
379C2×D8—121no—
380C2×D8—121no—
381C22×C8—31no—
382C22×C8—31no—
383C22×C8—62no—
384C22×C8—121no—
385C22×C8—121no—
386C22×C8C22×D311yescharacteristic
387C22×C8C22×D311yescharacteristic
388C4⋊Q8—22no—
389C4⋊Q8—22no—
390#123—68no—
391#123—68no—
392C22⋊Q8—68no—
393#121—34no—
394#121—62no—
395#121—62no—
396#121—62no—
397#121—62no—
398#121—62no—
399#121—121no—
400#121—121no—
401#120—124no—
402C4×D4—62no—
403C4×D4—62no—
404C4×D4—62no—
405C4×D4—62no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C4⋊C4C22×D311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—31no—
422C2×C22⋊C4—31no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C42C22×D311yescharacteristic
432#102—22no—
433#102—22no—
434#102—62no—
435#102—62no—
436#102—62no—
437#102—62no—
438#102—121no—
439#102—121no—
440C22⋊C8—62no—
441C22⋊C8—121no—
442C22⋊C8—121no—
443#95—61no—
444C23×C3—22no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3C22×D411yescharacteristic
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—48no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—84no—
478C22×D3—84no—
479C22×D3—84no—
480C22×D3—84no—
481C22×D3—84no—
482C22×D3—84no—
483C22×D3#12012yes—
484C22×D3C2×D812yes—
485C22×D3C2×D812yes—
486C22×D3AGL(1,ℤ/8)12yes—
487C3×Q8—48no—
488C3×D4—22no—
489C3×D4—22no—
490C3×D4—41no—
491C3×D4—41no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4C2×D812yes—
507C2×C3×C4C22×D411yescharacteristic
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C2×#4111yescharacteristic
510C2×C3×C4C2×#4111yescharacteristic
511C2×C3×C4H(5,𝔽2)11yescharacteristic
512C2×C3×C4H(5,𝔽2)11yescharacteristic
513#67—48no—
514#67—84no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—22no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3#12012yes—
527D12—28no—
528D12—22no—
529D12—22no—
530D12—22no—
531D12—22no—
532D12—48no—
533D12—48no—
534D12—41no—
535D12—41no—
536D12—41no—
537D12—41no—
538D12—84no—
539C4×D3—22no—
540C4×D3—22no—
541C4×D3—22no—
542C4×D3—22no—
543C4×D3—48no—
544C4×D3—48no—
545C4×D3—48no—
546C4×D3—41no—
547C4×D3—41no—
548C4×D3—41no—
549C4×D3—41no—
550C3×C8—41no—
551C3×C8—41no—
552C3⋊C8—41no—
553C3⋊C8—41no—
554C24—21no—
555C24—31no—
556C24—31no—
557C24—61no—
558C24—61no—
559C24—122no—
560C24—122no—
561C24—122no—
562C24—122no—
563C24—122no—
564C24—241no—
565C24—241no—
566#41—1232no—
567C2×Q8—24no—
568C2×Q8—42no—
569C2×Q8—42no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—34no—
576C2×D4—32no—
577C2×D4—32no—
578C2×D4—62no—
579C2×D4—62no—
580C2×D4—64no—
581C2×D4—64no—
582C2×D4—68no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—122no—
594C2×D4—122no—
595C2×D4—122no—
596C2×D4—122no—
597C2×D4—122no—
598C2×D4—122no—
599C2×D4—122no—
600C2×D4—124no—
601C2×D4—124no—
602C2×D4—124no—
603C2×D4—122no—
604C2×D4—122no—
605C2×D4—122no—
606C2×D4—122no—
607C2×D4—241no—
608C2×D4—241no—
609C2×D4#23912yescomplemented
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—31no—
614C22×C4—32no—
615C22×C4—32no—
616C22×C4—31no—
617C22×C4—64no—
618C22×C4—64no—
619C22×C4—64no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—122no—
633C22×C4—122no—
634C22×C4—122no—
635C22×C4—122no—
636C22×C4—122no—
637C22×C4—122no—
638C22×C4D3×D411yescharacteristic
639C22×C4D3×D411yescharacteristic
640C22×C4C23×D311yescharacteristic
641D8—124no—
642D8—124no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—61no—
650C2×C8—61no—
651C2×C8—61no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—124no—
656C4⋊C4—24no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—32no—
662C4⋊C4—64no—
663C4⋊C4—62no—
664C4⋊C4—64no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4D3×D412yes—
669C4⋊C4D3×D412yes—
670C22⋊C4—42no—
671C22⋊C4—62no—
672C22⋊C4—64no—
673C22⋊C4—62no—
674C22⋊C4—64no—
675C22⋊C4—64no—
676C22⋊C4—81no—
677C22⋊C4—122no—
678C22⋊C4—122no—
679C22⋊C4—122no—
680C22⋊C4—122no—
681C22⋊C4—241no—
682C42—21no—
683C42—21no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3C2×#12011yescharacteristic
692C22×C3#54611yescharacteristic
693C22×C3#54611yescharacteristic
694C22×C3C22×D811yescharacteristic
695C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
696C22×C3#57711yescharacteristic
697C22×C3#57711yescharacteristic
698C2×D3—22no—
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—22no—
702C2×D3—22no—
703C2×D3—22no—
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—42no—
717C2×D3—816no—
718C2×D3—81no—
719C2×D3—81no—
720C2×D3—81no—
721C2×D3—81no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C2×D3#44714yes—
727C3×C4—22no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—41no—
731C3×C4—81no—
732C3×C4#52511yescharacteristic
733C3×C4#53511yescharacteristic
734C3×C4#54611yescharacteristic
735C3×C4#54611yescharacteristic
736Dic3—22no—
737Dic3—41no—
738Dic3—42no—
739Dic3—81no—
740C23—22no—
741C23—32no—
742C23—32no—
743C23—32no—
744C23—32no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—62no—
762C23—62no—
763C23—128no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—121no—
771C23—121no—
772C23—121no—
773C23—121no—
774C23—121no—
775C23—121no—
776C23—244no—
777C23—244no—
778C23—244no—
779C23—244no—
780C23—244no—
781C23—244no—
782C23C2×D3×D411yescharacteristic
783Q8—48no—
784D4—22no—
785D4—22no—
786D4—41no—
787D4—41no—
788D4—68no—
789D4—62no—
790D4—62no—
791D4—62no—
792D4—62no—
793D4—128no—
794D4—128no—
795D4—128no—
796D4—121no—
797D4—121no—
798D4—121no—
799D4—121no—
800D4—244no—
801D4—244no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—32no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—62no—
826C2×C4—61no—
827C2×C4—128no—
828C2×C4—128no—
829C2×C4—128no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4—121no—
835C2×C4—121no—
836C2×C4—121no—
837C2×C4—121no—
838C2×C4—121no—
839C2×C4D3×D812yes—
840C2×C4C2×D3×D411yescharacteristic
841C2×C4C2×D3×D411yescharacteristic
842C2×C4C2×#23911yescharacteristic
843C2×C4D3×#4111yescharacteristic
844C2×C4#100911yescharacteristic
845C2×C4#100911yescharacteristic
846C8—41no—
847C8—41no—
848C8—121no—
849C8—121no—
850C2×C3—82no—
851C2×C3#240411yescharacteristic
852C2×C3C2×#44711yescharacteristic
853C2×C3#301011yescharacteristic
854C2×C3#329411yescharacteristic
855C2×C3#329411yescharacteristic
856C2×C3#330611yescharacteristic
857C2×C3#330611yescharacteristic
858D3—24no—
859D3—42no—
860D3—82no—
861D3—82no—
862C22—34no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—62no—
867C22—62no—
868C22—62no—
869C22—62no—
870C22—62no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—122no—
884C22—122no—
885C22—122no—
886C22—122no—
887C22—122no—
888C22—122no—
889C22—2416no—
890C22—241no—
891C22—241no—
892C22—241no—
893C22—241no—
894C22—241no—
895C22—241no—
896C22—241no—
897C22—241no—
898C22D3×#12011yescharacteristic
899C22#563011yescharacteristic
900C22#567611yescharacteristic
901C22C2×D3×D811yescharacteristic
902C22#576211yescharacteristic
903C22D3×AGL(1,ℤ/8)11yescharacteristic
904C22#577811yescharacteristic
905C4—22no—
906C4—42no—
907C4—42no—
908C4—41no—
909C4—62no—
910C4—81no—
911C4—121no—
912C4—122no—
913C4—241no—
914C4#562711yescharacteristic
915C4#563011yescharacteristic
916C4#567411yescharacteristic
917C4#567611yescharacteristic
918C3#2396011yescharacteristic, complemented, Sylow
919C2—64no—
920C2—82no—
921C2—122no—
922C2—242no—
923C2—242no—
924C2#7686311yescharacteristic
925C2D3×#44711yescharacteristic
926C2#8004111yescharacteristic
927C2#8098011yescharacteristic
928C2#8107711yescharacteristic
929C2#8157611yescharacteristic
930C2#8169611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2023C2
socleC23×C3C22×D4
hypercenter#2023D3
hypocenterC3#23960
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×#5726C2semidirect
2. C2×#4773C2semidirect
3. C2×D3×#102C2semidirect
4. #76436C2semidirect
5. C3×#2023C2semidirect
6. #71792C2semidirect
7. #70204C2semidirect
8. #70200C2semidirect
9. #69657C2semidirect
10. #68886C2semidirect
11. #68883C2semidirect
12. #68880C2semidirect
13. #68871C2semidirect
14. #68673C2semidirect
15. #68668C2semidirect
19. C2×C3×C4⋊Q8C22semidirect
29. C2×#895C22semidirect
33. C2×D3×C4⋊C4C22semidirect
36. C2×C4×D12C22semidirect
42. C2×#821C22semidirect
44. C2×(C2×D3)⋊C8C22semidirect
45. C2×(C2×D3)⋊C8C22semidirect
49. C2×#809C22semidirect
56. C3×#340C22semidirect
57. C3×#340C22semidirect
58. C3×#336C22semidirect
59. #4551C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4524C22semidirect
69. #2023D3semidirect
149. #895D4semidirect
155. D3×C4⋊C4D4semidirect
180. C2×C4⋊Q8C2×D3semidirect
216. #340C2×D3semidirect
217. #340C2×D3semidirect
219. #336C2×D3semidirect
240. C2×C3×D4#41semidirect
283. C2×D12D8semidirect
285. C2×D12#41semidirect
609. C2×D4#239semidirect
918. C3#23960semidirect

Maximal subgroups

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

subgroupindex
C2×#57262
C2×#47732
C2×D3×#1022
#764362
C3×#20232
#717922
#702042
#702002
#696572
#688862
#688832
#688802
#688712
#686732
#686682
#239603