Finite Group Databasebeta

← #10827333

Subgroups — #10827333

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×#5611C211yesmaximal, characteristic, complemented
2C2×#5156C211yesmaximal, characteristic, complemented
3#82640C211yesmaximal, characteristic, complemented
4C2×D3×#102C211yesmaximal, characteristic, complemented
5C3×#1999C211yesmaximal, characteristic, complemented
6#72037C211yesmaximal, characteristic, complemented
7#71684C211yesmaximal, characteristic, complemented
8#71677C211yesmaximal, characteristic, complemented
9#70202C211yesmaximal, characteristic, complemented
10#70172C211yesmaximal, characteristic, complemented
11#70163C211yesmaximal, characteristic, complemented
12#69957C211yesmaximal, characteristic, complemented
13#69932C211yesmaximal, characteristic, complemented
14#68898C211yesmaximal, characteristic, complemented
15#68871C211yesmaximal, characteristic, complemented
16#23960—31nomaximal, Sylow
17C22×#237—21no—
18C22×D3×D4C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic, complemented
22C2×#938C2211yescharacteristic
23C2×#937—21no—
24C2×#935—21no—
25C2×D4×Dic3C2211yescharacteristic, complemented
26C22×#213C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C2×C4×#67C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic, complemented
30C22×D3×C8C2211yescharacteristic
31#5611—24no—
32#5611—24no—
33C2×D3×C4⋊C4C2211yescharacteristic
34C2×#888C2211yescharacteristic, complemented
35C2×#883—21no—
36C2×#878—21no—
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic, complemented
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40#5223—21no—
41#5221C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic, complemented
45C2×#830C2211yescharacteristic, complemented
46#5156—24no—
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50#4988C2211yescharacteristic
51#4987C2211yescharacteristic
52C2×#809C2211yescharacteristic
53#4959—21no—
54#4955—21no—
55D3×#102—24no—
56C3×#340C2211yescharacteristic, complemented
57#4551C2211yescharacteristic, complemented
58#4551C2211yescharacteristic, complemented
59#4550C2211yescharacteristic, complemented
60#4550C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64C2×#547—31no—
65C2×#447—31no—
66C22×#102—31no—
67#2408—31no—
68#2023—31no—
69#2023—31no—
70#1999—31no—
71#1999D311yescharacteristic, complemented
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×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C22×#67—21no—
88C22×#67D411yescharacteristic
89C23×Dic3—21no—
90C23×Dic3—21no—
91C2×#237—28no—
92C2×#237—44no—
93C2×#237—44no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—22no—
97C2×D3×D4—22no—
98C2×D3×D4—41no—
99C2×D3×D4—41no—
100C22×D12C2311yescharacteristic
101C22×C4×D3—21no—
102C22×C4×D3C2311yescharacteristic
103C22×Dic6—21no—
104C2×C3×D8—22no—
105C2×C3×D8—22no—
106C2×C3×D8—41no—
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C3×#121—22no—
110C3×#121—22no—
111C3×#121—22no—
112C3×#121—41no—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#217—21no—
120C2×#217—21no—
121C2×#217D411yescharacteristic
122#938—22no—
123#938D414yescomplemented
124#937—44no—
125#935—28no—
126D4×Dic3—22no—
127D4×Dic3—22no—
128C2×#213—22no—
129C2×#213—22no—
130C2×#213—41no—
131#930—22no—
132#930—41no—
133C4×#67—22no—
134C4×#67—22no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4D411yescharacteristic
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3—22no—
142C2×C4⋊Dic3—22no—
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4D411yescharacteristic
149C2×C4×Dic3C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C2×D3×C8—22no—
153C2×D3×C8—41no—
154C2×D3×C8—41no—
155D3×C4⋊C4—22no—
156D3×C4⋊C4D414yescomplemented
157#888—22no—
158#888—22no—
159#883—28no—
160#878—28no—
161C3×#102—22no—
162C3×#102—41no—
163C3×C22⋊C8—41no—
164#832—22no—
165#832—22no—
166#832—41no—
167C3⋊#95—21no—
168#830—41no—
169#821—22no—
170#821—22no—
171(C2×D3)⋊C8—22no—
172#809—22no—
173C22×#41—61no—
174C23×D4—31no—
175C22×D8—31no—
176C22×D8C2×D311yescharacteristic
177C23×C8—31no—
178#547—64no—
179#547—64no—
180C2×C4⋊Q8—31no—
181C2×#123—61no—
182C2×#123—61no—
183C2×C22⋊Q8—61no—
184C2×#121—31no—
185C2×#121—31no—
186C2×#121C2×D311yescharacteristic
187C2×#121C2×D311yescharacteristic, complemented
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, complemented
203C2×C22⋊C8—31no—
204C2×C22⋊C8—31no—
205C2×C22⋊C8C2×D311yescharacteristic, complemented
206#394—61no—
207#392—61no—
208#390—31no—
209#390—31no—
210#380—31no—
211#379—61no—
212#340—31no—
213#340—31no—
214#340—31no—
215#340—31no—
216#340—31no—
217#340C2×D311yescharacteristic, complemented
218#336—31no—
219#336—31no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3C2×D411yescharacteristic
223C23×D3—21no—
224C23×D3—42no—
225C23×D3—42no—
226C23×D3—42no—
227C23×D3—42no—
228C23×D3—42no—
229C23×D3—81no—
230C23×D3—81no—
231C23×D3C2×D411yescharacteristic
232C2×C3×D4—24no—
233C2×C3×D4—21no—
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—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4—42no—
246C2×C3×D4—42no—
247C2×C3×D4—81no—
248C2×C3×D4C2×D412yes—
249C2×C3×D4#4112yescomplemented
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C2×#67—22no—
261C2×#67—22no—
262C2×#67—24no—
263C2×#67—42no—
264C2×#67—42no—
265C2×#67—42no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67—42no—
269C2×#67—42no—
270C2×#67—81no—
271C2×#67D814yescomplemented
272C22×Dic3—24no—
273C22×Dic3—24no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—42no—
278C22×Dic3—42no—
279C22×Dic3—42no—
280C22×Dic3—42no—
281C22×Dic3C2×D411yescharacteristic
282C22×Dic3C2×D411yescharacteristic
283C22×Dic3C2×D411yescharacteristic
284#237—432no—
285D3×D4—28no—
286D3×D4—44no—
287D3×D4—44no—
288D3×D4—44no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—21no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12#4112yescomplemented
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—24no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×C4×D3C2×D412yes—
303C2×C4×D3C2×D412yes—
304C2×Dic6—24no—
305C2×Dic6—42no—
306C2×Dic6—42no—
307C3×D8—44no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4C2×D412yes—
318C3×C22⋊C4—24no—
319C3×C22⋊C4—42no—
320#217—24no—
321#217—24no—
322#217—22no—
323#217—42no—
324#217—81no—
325#213—44no—
326(C2×D3)⋊C4—22no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4—42no—
329(C2×D3)⋊C4—42no—
330(C2×D3)⋊C4—81no—
331C4⋊Dic3—24no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3C2×D412yes—
337C4⋊Dic3C2×D412yes—
338Dic3⋊C4—24no—
339Dic3⋊C4—22no—
340Dic3⋊C4—24no—
341C4×Dic3—21no—
342C4×Dic3—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349D3×C8—44no—
350C25—61no—
351C2×#41—68no—
352C2×#41—124no—
353C2×#41—124no—
354C22×Q8—61no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—31no—
358C22×D4—31no—
359C22×D4—62no—
360C22×D4—62no—
361C22×D4—61no—
362C22×D4—62no—
363C22×D4—62no—
364C22×D4—61no—
365C22×D4—61no—
366C22×D4—121no—
367C22×D4—121no—
368C22×D4C22×D311yescharacteristic
369C22×D4C22×D311yescharacteristic
370C23×C4—31no—
371C23×C4—61no—
372C23×C4—61no—
373C23×C4—61no—
374C23×C4C22×D311yescharacteristic
375C2×D8—22no—
376C2×D8—22no—
377C2×D8—41no—
378C2×D8—62no—
379C2×D8—62no—
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—62no—
389C4⋊Q8—62no—
390#123—68no—
391#123—68no—
392C22⋊Q8—68no—
393#121—22no—
394#121—22no—
395#121—22no—
396#121—34no—
397#121—41no—
398#121—62no—
399#121—62no—
400#121—121no—
401#120—124no—
402C4×D4—62no—
403C4×D4—62no—
404C4×D4—62no—
405C4×D4—62no—
406C2×C4⋊C4—31no—
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—62no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—61no—
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×C42—31no—
432#102—22no—
433#102—41no—
434#102—62no—
435#102—62no—
436#102—62no—
437#102—62no—
438#102—62no—
439#102—121no—
440C22⋊C8—41no—
441C22⋊C8—62no—
442C22⋊C8—121no—
443#95—61no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3C2×D812yes—
465C23×C3C22×D411yescharacteristic
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—22no—
471C22×D3—48no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—84no—
479C22×D3—84no—
480C22×D3—84no—
481C22×D3—84no—
482C22×D3—84no—
483C22×D3—84no—
484C22×D3#12012yes—
485C22×D3C2×D812yes—
486C22×D3AGL(1,ℤ/8)12yes—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—22no—
490C3×D4—22no—
491C3×D4—48no—
492C3×D4—41no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—84no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4C2×#4111yescharacteristic
513C2×C3×C4C2×#4111yescharacteristic
514C2×C3×C4H(5,𝔽2)11yescharacteristic
515C2×C3×C4H(5,𝔽2)11yescharacteristic
516#67—28no—
517#67—48no—
518#67—48no—
519#67—84no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—48no—
530C2×Dic3—48no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3#12012yes—
539C2×Dic3C2×D812yes—
540D12—22no—
541D12—22no—
542D12—41no—
543D12—41no—
544C4×D3—22no—
545C4×D3—22no—
546C4×D3—22no—
547C4×D3—22no—
548C4×D3—48no—
549Dic6—48no—
550C3×C8—41no—
551C3×C8—41no—
552C3⋊C8—41no—
553C3⋊C8—41no—
554C24—21no—
555C24—21no—
556C24—31no—
557C24—61no—
558C24—122no—
559C24—122no—
560C24—122no—
561C24—122no—
562C24—122no—
563C24—241no—
564C24—241no—
565C24D3×D411yescharacteristic
566#41—1232no—
567C2×Q8—64no—
568C2×Q8—122no—
569C2×Q8—122no—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—34no—
582C2×D4—32no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—68no—
588C2×D4—62no—
589C2×D4—62no—
590C2×D4—64no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—81no—
597C2×D4—122no—
598C2×D4—124no—
599C2×D4—124no—
600C2×D4—124no—
601C2×D4—122no—
602C2×D4—122no—
603C2×D4—122no—
604C2×D4—122no—
605C2×D4—122no—
606C2×D4—122no—
607C2×D4—241no—
608C2×D4D3×D412yes—
609C2×D4#23712yescomplemented
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—32no—
621C22×C4—32no—
622C22×C4—31no—
623C22×C4—64no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—64no—
629C22×C4—64no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—122no—
634C22×C4—122no—
635C22×C4—122no—
636C22×C4—122no—
637C22×C4—122no—
638C22×C4—122no—
639C22×C4D3×D411yescharacteristic
640C22×C4C23×D311yescharacteristic
641D8—44no—
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—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—32no—
660C4⋊C4—32no—
661C4⋊C4—64no—
662C4⋊C4—62no—
663C4⋊C4—64no—
664C4⋊C4—64no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4D3×D412yes—
670C22⋊C4—24no—
671C22⋊C4—42no—
672C22⋊C4—62no—
673C22⋊C4—62no—
674C22⋊C4—64no—
675C22⋊C4—64no—
676C22⋊C4—122no—
677C22⋊C4—122no—
678C22⋊C4—122no—
679C22⋊C4—122no—
680C22⋊C4—241no—
681C22⋊C4—241no—
682C42—61no—
683C42—61no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—81no—
701C22×C3—81no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3C2×#12011yescharacteristic
706C22×C3#54611yescharacteristic
707C22×C3#54611yescharacteristic
708C22×C3C22×D811yescharacteristic
709C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
710C22×C3#57711yescharacteristic
711C22×C3#57711yescharacteristic
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—816no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C2×D3#44714yes—
727C3×C4—41no—
728C3×C4—42no—
729C3×C4—81no—
730C3×C4#52511yescharacteristic
731C3×C4#53511yescharacteristic
732C3×C4#54611yescharacteristic
733C3×C4#54611yescharacteristic
734Dic3—22no—
735Dic3—22no—
736Dic3—42no—
737Dic3—42no—
738Dic3—41no—
739Dic3—81no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—22no—
748C23—32no—
749C23—32no—
750C23—32no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—61no—
764C23—61no—
765C23—61no—
766C23—61no—
767C23—62no—
768C23—128no—
769C23—121no—
770C23—121no—
771C23—121no—
772C23—121no—
773C23—121no—
774C23—121no—
775C23—244no—
776C23—244no—
777C23—244no—
778C23—244no—
779C23—244no—
780C23—244no—
781C23D3×D812yes—
782C23C2×D3×D411yescharacteristic
783Q8—128no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—48no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—68no—
794D4—62no—
795D4—62no—
796D4—84no—
797D4—128no—
798D4—128no—
799D4—121no—
800D4—121no—
801D4—244no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—41no—
809C2×C4—41no—
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—61no—
820C2×C4—61no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—128no—
831C2×C4—128no—
832C2×C4—128no—
833C2×C4—121no—
834C2×C4—121no—
835C2×C4—121no—
836C2×C4—121no—
837C2×C4—121no—
838C2×C4—121no—
839C2×C4—121no—
840C2×C4C2×D3×D411yescharacteristic
841C2×C4C2×D3×D411yescharacteristic
842C2×C4C2×#23711yescharacteristic
843C2×C4#100411yescharacteristic
844C2×C4#100411yescharacteristic
845C2×C4D3×#4111yescharacteristic
846C8—41no—
847C8—41no—
848C8—121no—
849C8—121no—
850C2×C3—42no—
851C2×C3—82no—
852C2×C3—82no—
853C2×C3#240411yescharacteristic
854C2×C3C2×#44711yescharacteristic
855C2×C3#301011yescharacteristic
856C2×C3#329411yescharacteristic
857C2×C3#329411yescharacteristic
858C2×C3#330611yescharacteristic
859C2×C3#330611yescharacteristic
860D3—24no—
861D3—82no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—34no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—62no—
877C22—62no—
878C22—62no—
879C22—62no—
880C22—62no—
881C22—62no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—122no—
891C22—122no—
892C22—122no—
893C22—2416no—
894C22—241no—
895C22—241no—
896C22—241no—
897C22—241no—
898C22D3×#12011yescharacteristic
899C22#559111yescharacteristic
900C22#561011yescharacteristic
901C22C2×D3×D811yescharacteristic
902C22#577011yescharacteristic
903C22D3×AGL(1,ℤ/8)11yescharacteristic
904C22#577511yescharacteristic
905C4—42no—
906C4—41no—
907C4—62no—
908C4—62no—
909C4—81no—
910C4—122no—
911C4—122no—
912C4—121no—
913C4—241no—
914C4#559111yescharacteristic
915C4#560611yescharacteristic
916C4#561011yescharacteristic
917C4#571511yescharacteristic
918C3#2396011yescharacteristic, complemented, Sylow
919C2—42no—
920C2—64no—
921C2—82no—
922C2—82no—
923C2—242no—
924C2#7675411yescharacteristic
925C2D3×#44711yescharacteristic
926C2#8001411yescharacteristic
927C2#8008611yescharacteristic
928C2#8010611yescharacteristic
929C2#8073111yescharacteristic
930C2#8087411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1999C2
socleC23×C3C22×D4
hypercenter#1999D3
hypocenterC3#23960
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. C2×#5611C2semidirect
2. C2×#5156C2semidirect
3. #82640C2semidirect
4. C2×D3×#102C2semidirect
5. C3×#1999C2semidirect
6. #72037C2semidirect
7. #71684C2semidirect
8. #71677C2semidirect
9. #70202C2semidirect
10. #70172C2semidirect
11. #70163C2semidirect
12. #69957C2semidirect
13. #69932C2semidirect
14. #68898C2semidirect
15. #68871C2semidirect
21. C2×C3×#121C22semidirect
25. C2×D4×Dic3C22semidirect
29. C22×C4⋊Dic3C22semidirect
34. C2×#888C22semidirect
38. C2×C3×#102C22semidirect
39. C2×C3×C22⋊C8C22semidirect
44. C2×#832C22semidirect
45. C2×#830C22semidirect
56. C3×#340C22semidirect
57. #4551C22semidirect
58. #4551C22semidirect
59. #4550C22semidirect
60. #4550C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4529C22semidirect
71. #1999D3semidirect
123. #938D4semidirect
156. D3×C4⋊C4D4semidirect
187. C2×#121C2×D3semidirect
202. C2×#102C2×D3semidirect
205. C2×C22⋊C8C2×D3semidirect
217. #340C2×D3semidirect
249. C2×C3×D4#41semidirect
271. C2×#67D8semidirect
294. C2×D12#41semidirect
609. C2×D4#237semidirect
918. C3#23960semidirect

Maximal subgroups

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

subgroupindex
C2×#56112
C2×#51562
#826402
C2×D3×#1022
C3×#19992
#720372
#716842
#716772
#702022
#701722
#701632
#699572
#699322
#688982
#688712
#239603