Finite Group Databasebeta

← #10828124

Subgroups — #10828124

Order 768.

1822 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
1C2×D4×#67C211yesmaximal, characteristic
2C2×#4774C211yesmaximal, characteristic, complemented
3C2×D3×#102C211yesmaximal, characteristic, complemented
4#73911C211yesmaximal, characteristic, complemented
5C3×#1786C211yesmaximal, characteristic, complemented
6#72128C211yesmaximal, characteristic, complemented
7#70211C211yesmaximal, characteristic, complemented
8#70202C211yesmaximal, characteristic, complemented
9#70198C211yesmaximal, characteristic, complemented
10#70177C211yesmaximal, characteristic, complemented
11#70168C211yesmaximal, characteristic, complemented
12#70167C211yesmaximal, characteristic, complemented
13#69957C211yesmaximal, characteristic, complemented
14#69934C211yesmaximal, characteristic, complemented
15#69523C211yesmaximal, characteristic, complemented
16#24032—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×#67—21no—
19C22×D3×D4C2211yescharacteristic
20C2×#953—21no—
21C2×#940C2211yescharacteristic
22C2×#939—21no—
23D4×#67—24no—
24D4×#67—24no—
25C2×#938C2211yescharacteristic
26C2×#937—21no—
27C2×D4×Dic3C2211yescharacteristic
28C2×#930C2211yescharacteristic
29C2×C4×#67C2211yescharacteristic
30C22×D3×C8C2211yescharacteristic, complemented
31C2×D3×C4⋊C4C2211yescharacteristic, complemented
32C2×#883—21no—
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic, complemented
36C2×C3×#102C2211yescharacteristic, complemented
37C2×C3×C22⋊C8C2211yescharacteristic, complemented
38C3×#380C2211yescharacteristic, complemented
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic, complemented
42C2×#832C2211yescharacteristic, complemented
43#5212C2211yescharacteristic, complemented
44C2×#830C2211yescharacteristic, complemented
45C2×#821C2211yescharacteristic, complemented
46C2×#821C2211yescharacteristic, complemented
47C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
48C2×#818C2211yescharacteristic, complemented
49#4987C2211yescharacteristic, complemented
50#4984C2211yescharacteristic, complemented
51#4972C2211yescharacteristic, complemented
52C2×#809C2211yescharacteristic, complemented
53C2×#809C2211yescharacteristic, complemented
54C2×#807C2211yescharacteristic, complemented
55#4952—21no—
56#4774—24no—
57D3×#102—24no—
58#4664—21no—
59#4657—21no—
60#4551C2211yescharacteristic, complemented
61#4550C2211yescharacteristic, complemented
62#4550C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64C2×D42—31no—
65C2×#480—31no—
66C22×#102—31no—
67#2486—31no—
68#2041—31no—
69#2041—31no—
70#2033—31no—
71#2033—31no—
72#1893—31no—
73#1869—31no—
74#1862—31no—
75#1862—31no—
76#1786—31no—
77#1786—31no—
78#1786D311yescharacteristic, complemented
79C25×C3—21no—
80C24×D3—21no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—21no—
86C22×C3×D4—41no—
87C22×C3×D4—41no—
88C22×C3×D4C2311yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C22×#67—28no—
92C22×#67—21no—
93C22×#67—21no—
94C22×#67—21no—
95C22×#67—21no—
96C22×#67—21no—
97C22×#67—44no—
98C22×#67—44no—
99C22×#67D411yescharacteristic
100C23×Dic3—21no—
101C2×D3×D4—22no—
102C2×D3×D4—22no—
103C2×D3×D4—22no—
104C2×D3×D4—41no—
105C2×D3×D4—41no—
106C2×D3×D4D414yes—
107C22×D12C2311yescharacteristic
108C22×C4×D3—21no—
109C22×C4×D3C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C22×C3×C8C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115#953—28no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#217D411yescharacteristic
120#940—22no—
121#940—22no—
122#939—28no—
123#938—22no—
124#938D414yes—
125#937—28no—
126D4×Dic3—22no—
127D4×Dic3—22no—
128#930—22no—
129#930—22no—
130C4×#67—22no—
131C4×#67—22no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4D411yescharacteristic
135C2×C4⋊Dic3—21no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4D411yescharacteristic
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D3×C8—22no—
146C2×D3×C8—41no—
147C2×D3×C8—41no—
148D3×C4⋊C4—22no—
149D3×C4⋊C4—22no—
150#883—44no—
151C3×#102—22no—
152C3×#102—22no—
153C3×#102—22no—
154C3×#102—41no—
155C3×C22⋊C8—41no—
156C3×#95—21no—
157#832—22no—
158#832—22no—
159#832—22no—
160#832—41no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165#830—41no—
166#821—22no—
167#821—41no—
168(C2×D3)⋊C8—22no—
169#818—22no—
170#809—22no—
171#809—41no—
172#807—22no—
173C23×D4—31no—
174C23×D4—61no—
175C23×D4C2×D311yescharacteristic
176C23×C8—31no—
177D42—64no—
178D42—64no—
179C2×#127—31no—
180C2×#123—61no—
181C2×#121—31no—
182C2×#121—31no—
183C2×#121—61no—
184C2×#120—61no—
185C2×#120—61no—
186C2×C4×D4—31no—
187C2×C4×D4—31no—
188C22×C4⋊C4—31no—
189#480—64no—
190C2×#107—31no—
191C2×#107—31no—
192C2×#102—31no—
193C2×#102—31no—
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×#102C2×D311yescharacteristic, complemented
204C2×#102C2×D311yescharacteristic, complemented
205C2×C22⋊C8—31no—
206C2×C22⋊C8—31no—
207C2×C22⋊C8C2×D311yescharacteristic, complemented
208#398—61no—
209#397—61no—
210#389—31no—
211#389—31no—
212#381—61no—
213#380—31no—
214#380—31no—
215#380C2×D311yescharacteristic, complemented
216#340—31no—
217#340—31no—
218#336—31no—
219#336—31no—
220C24×C3—21no—
221C24×C3—24no—
222C24×C3—21no—
223C24×C3—42no—
224C24×C3—42no—
225C24×C3—42no—
226C24×C3—42no—
227C24×C3—81no—
228C24×C3—81no—
229C24×C3C2×D411yescharacteristic
230C23×D3—21no—
231C23×D3—24no—
232C23×D3—42no—
233C23×D3—42no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—81no—
237C23×D3—81no—
238C23×D3C2×D411yescharacteristic
239C2×C3×D4—24no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—42no—
249C2×C3×D4—42no—
250C2×C3×D4—44no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4—44no—
254C2×C3×D4C2×D412yes—
255C2×C3×D4C2×D412yes—
256C2×C3×D4#4112yes—
257C2×C3×D4#4112yes—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C2×#67—22no—
269C2×#67—22no—
270C2×#67—24no—
271C2×#67—24no—
272C2×#67—24no—
273C2×#67—24no—
274C2×#67—24no—
275C2×#67—42no—
276C2×#67—42no—
277C2×#67—42no—
278C2×#67—432no—
279C2×#67—42no—
280C2×#67—42no—
281C2×#67—42no—
282C2×#67—42no—
283C2×#67—42no—
284C2×#67—81no—
285C2×#67—81no—
286C2×#67D814yes—
287C22×Dic3—24no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—42no—
292C22×Dic3—42no—
293C22×Dic3C2×D411yescharacteristic
294C22×Dic3C2×D411yescharacteristic
295C22×Dic3C2×D411yescharacteristic
296D3×D4—28no—
297D3×D4—44no—
298D3×D4—44no—
299D3×D4—44no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12C2×D412yes—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—42no—
311C2×C4×D3—42no—
312C2×C4×D3—42no—
313C2×C4×D3C2×D412yes—
314C2×C4×D3C2×D412yes—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C22⋊C4—42no—
326#217—24no—
327#217—22no—
328#217—24no—
329#217—42no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—22no—
332(C2×D3)⋊C4—42no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3—21no—
338C4⋊Dic3—42no—
339C4⋊Dic3C2×D412yes—
340Dic3⋊C4—22no—
341Dic3⋊C4—42no—
342Dic3⋊C4—42no—
343C4×Dic3—21no—
344C4×Dic3—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351D3×C8—44no—
352C25—21no—
353C25—61no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—21no—
359C22×D4—31no—
360C22×D4—34no—
361C22×D4—31no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4—62no—
365C22×D4—61no—
366C22×D4—61no—
367C22×D4—61no—
368C22×D4—62no—
369C22×D4—62no—
370C22×D4—61no—
371C22×D4—68no—
372C22×D4—61no—
373C22×D4—121no—
374C22×D4—121no—
375C22×D4—124no—
376C22×D4—124no—
377C22×D4C22×D311yescharacteristic
378C22×D4C22×D311yescharacteristic
379C23×C4—31no—
380C23×C4—61no—
381C23×C4—61no—
382C23×C4C22×D311yescharacteristic
383C22×C8—31no—
384C22×C8—31no—
385C22×C8—62no—
386C22×C8—121no—
387C22×C8—121no—
388C22×C8C22×D311yescharacteristic
389C22×C8C22×D311yescharacteristic
390#127—62no—
391#127—62no—
392#123—124no—
393#121—34no—
394#121—62no—
395#121—62no—
396#121—62no—
397#121—68no—
398#120—68no—
399#120—68no—
400C4×D4—62no—
401C4×D4—62no—
402C4×D4—62no—
403C4×D4—62no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C4⋊C4—61no—
411C2×C4⋊C4—61no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4C22×D311yescharacteristic
414C2×C4⋊C4C22×D311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—31no—
417C2×C22⋊C4—31no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C42—31no—
424#107—62no—
425#107—62no—
426#102—22no—
427#102—22no—
428#102—22no—
429#102—41no—
430#102—62no—
431#102—62no—
432#102—62no—
433#102—62no—
434#102—62no—
435#102—121no—
436#102—121no—
437#102—121no—
438C22⋊C8—41no—
439C22⋊C8—62no—
440C22⋊C8—121no—
441#95—21no—
442#95—61no—
443#95—61no—
444#95—61no—
445#95—61no—
446C23×C3—22no—
447C23×C3—21no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—22no—
456C23×C3—48no—
457C23×C3—48no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—84no—
469C23×C3—84no—
470C23×C3—84no—
471C23×C3—84no—
472C23×C3—84no—
473C23×C3C2×D812yes—
474C23×C3C22×D411yescharacteristic
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—22no—
480C22×D3—48no—
481C22×D3—41no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—48no—
488C22×D3—84no—
489C22×D3—84no—
490C22×D3—84no—
491C22×D3—84no—
492C22×D3—84no—
493C22×D3#12012yes—
494C22×D3C2×D812yes—
495C22×D3AGL(1,ℤ/8)12yes—
496C3×D4—22no—
497C3×D4—22no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—22no—
501C3×D4—48no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4#12314yescomplemented
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
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×C4C22×D411yescharacteristic
519C2×C3×C4C22×D411yescharacteristic
520C2×C3×C4C2×#4111yescharacteristic
521C2×C3×C4C2×#4111yescharacteristic
522C2×C3×C4H(5,𝔽2)11yescharacteristic
523C2×C3×C4H(5,𝔽2)11yescharacteristic
524#67—28no—
525#67—48no—
526#67—48no—
527#67—48no—
528#67—48no—
529#67—84no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—22no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—48no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3#12012yes—
548C2×Dic3C2×D812yes—
549D12—22no—
550D12—22no—
551D12—41no—
552D12—41no—
553C4×D3—22no—
554C4×D3—22no—
555C4×D3—22no—
556C4×D3—22no—
557C4×D3—84no—
558C3×C8—41no—
559C3×C8—41no—
560C3⋊C8—41no—
561C3⋊C8—41no—
562C24—21no—
563C24—24no—
564C24—21no—
565C24—31no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—64no—
571C24—61no—
572C24—81no—
573C24—81no—
574C24—122no—
575C24—122no—
576C24—122no—
577C24—122no—
578C24—241no—
579C24—241no—
580C24D3×D411yescharacteristic
581C2×D4—24no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—34no—
591C2×D4—32no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—44no—
595C2×D4—44no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—64no—
599C2×D4—62no—
600C2×D4—62no—
601C2×D4—68no—
602C2×D4—64no—
603C2×D4—64no—
604C2×D4—64no—
605C2×D4—64no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—122no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—122no—
616C2×D4—122no—
617C2×D4—122no—
618C2×D4—1232no—
619C2×D4—122no—
620C2×D4—122no—
621C2×D4—122no—
622C2×D4—122no—
623C2×D4—241no—
624C2×D4—241no—
625C2×D4#23512yes—
626C2×D4D3×D412yes—
627C2×D4D3×D412yes—
628C2×D4#23712yes—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—31no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—64no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—122no—
651C22×C4—122no—
652C22×C4—122no—
653C22×C4—122no—
654C22×C4—122no—
655C22×C4D3×D411yescharacteristic
656C22×C4C23×D311yescharacteristic
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—61no—
664C2×C8—61no—
665C2×C8—61no—
666C2×C8—61no—
667C2×C8—61no—
668C2×C8—61no—
669C2×C8—124no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—32no—
675C4⋊C4—62no—
676C4⋊C4—61no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—122no—
682C4⋊C4—122no—
683C4⋊C4—122no—
684C22⋊C4—42no—
685C22⋊C4—62no—
686C22⋊C4—64no—
687C22⋊C4—62no—
688C22⋊C4—64no—
689C22⋊C4—64no—
690C22⋊C4—122no—
691C22⋊C4—122no—
692C42—61no—
693C42—61no—
694C22×C3—24no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—41no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—41no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—816no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3C2×#12011yescharacteristic
717C22×C3#54611yescharacteristic
718C22×C3#54611yescharacteristic
719C22×C3C22×D811yescharacteristic
720C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
721C22×C3#57711yescharacteristic
722C22×C3#57711yescharacteristic
723C2×D3—22no—
724C2×D3—22no—
725C2×D3—22no—
726C2×D3—22no—
727C2×D3—22no—
728C2×D3—22no—
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—42no—
732C2×D3—816no—
733C2×D3—81no—
734C2×D3—81no—
735C2×D3—81no—
736C2×D3—81no—
737C2×D3#44714yes—
738C3×C4—41no—
739C3×C4—81no—
740C3×C4—81no—
741C3×C4C2×#12311yescharacteristic
742C3×C4#53411yescharacteristic
743C3×C4#54611yescharacteristic
744C3×C4#54611yescharacteristic
745Dic3—22no—
746Dic3—22no—
747Dic3—42no—
748Dic3—41no—
749Dic3—81no—
750Dic3—81no—
751C23—21no—
752C23—22no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—22no—
760C23—22no—
761C23—32no—
762C23—32no—
763C23—32no—
764C23—48no—
765C23—48no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—61no—
777C23—61no—
778C23—61no—
779C23—61no—
780C23—62no—
781C23—84no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—128no—
787C23—128no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—121no—
793C23—121no—
794C23—244no—
795C23—244no—
796C23—244no—
797C23—244no—
798C23—244no—
799C23D3×D812yes—
800C23C2×D3×D411yescharacteristic
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—48no—
807D4—41no—
808D4—41no—
809D4—68no—
810D4—62no—
811D4—62no—
812D4—128no—
813D4—128no—
814D4—128no—
815D4—128no—
816D4—121no—
817D4—121no—
818D4—244no—
819D4#88314yescomplemented
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—61no—
836C2×C4—61no—
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—62no—
847C2×C4—128no—
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—244no—
857C2×C4C2×#23511yescharacteristic
858C2×C4C2×D3×D411yescharacteristic
859C2×C4C2×D3×D411yescharacteristic
860C2×C4C2×#23711yescharacteristic
861C2×C4#100411yescharacteristic
862C2×C4#100411yescharacteristic
863C8—41no—
864C8—41no—
865C8—121no—
866C8—121no—
867C2×C3—44no—
868C2×C3—42no—
869C2×C3—82no—
870C2×C3#240511yescharacteristic
871C2×C3C2×#44711yescharacteristic
872C2×C3#300911yescharacteristic
873C2×C3#329411yescharacteristic
874C2×C3#329411yescharacteristic
875C2×C3#331011yescharacteristic
876C2×C3#331011yescharacteristic
877D3—24no—
878D3—82no—
879C22—24no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—34no—
884C22—41no—
885C22—42no—
886C22—41no—
887C22—42no—
888C22—41no—
889C22—42no—
890C22—41no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—816no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—2416no—
912C22—241no—
913C22—241no—
914C22—241no—
915C22—241no—
916C22#549011yescharacteristic
917C22D3×#12011yescharacteristic
918C22#559111yescharacteristic
919C22C2×D3×D811yescharacteristic
920C22#576211yescharacteristic
921C22D3×AGL(1,ℤ/8)11yescharacteristic
922C22#577511yescharacteristic
923C4—41no—
924C4—62no—
925C4—62no—
926C4—81no—
927C4—81no—
928C4—121no—
929C4—122no—
930C4—241no—
931C4—241no—
932C4C2×#88311yescharacteristic
933C4#549011yescharacteristic
934C4#558911yescharacteristic
935C4#559111yescharacteristic
936C3#2403211yescharacteristic, complemented, Sylow
937C2—42no—
938C2—44no—
939C2—64no—
940C2—82no—
941C2—242no—
942C2#7385311yescharacteristic
943C2#7875711yescharacteristic
944C2#7893411yescharacteristic
945C2D3×#44711yescharacteristic
946C2#8001411yescharacteristic
947C2#8014811yescharacteristic
948C2#8016111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1786C2
socleC23×C3C22×D4
prime radicalC2×D4×#67C2
hypercenter#1786D3
hypocenterC3#24032
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#4774C2semidirect
3. C2×D3×#102C2semidirect
4. #73911C2semidirect
5. C3×#1786C2semidirect
6. #72128C2semidirect
7. #70211C2semidirect
8. #70202C2semidirect
9. #70198C2semidirect
10. #70177C2semidirect
11. #70168C2semidirect
12. #70167C2semidirect
13. #69957C2semidirect
14. #69934C2semidirect
15. #69523C2semidirect
30. C22×D3×C8C22semidirect
31. C2×D3×C4⋊C4C22semidirect
35. C2×C3×#102C22semidirect
36. C2×C3×#102C22semidirect
37. C2×C3×C22⋊C8C22semidirect
38. C3×#380C22semidirect
41. C2×#832C22semidirect
42. C2×#832C22semidirect
43. #5212C22semidirect
44. C2×#830C22semidirect
45. C2×#821C22semidirect
46. C2×#821C22semidirect
47. C2×(C2×D3)⋊C8C22semidirect
48. C2×#818C22semidirect
49. #4987C22semidirect
50. #4984C22semidirect
51. #4972C22semidirect
52. C2×#809C22semidirect
53. C2×#809C22semidirect
54. C2×#807C22semidirect
60. #4551C22semidirect
61. #4550C22semidirect
62. #4550C22semidirect
63. #4529C22semidirect
78. #1786D3semidirect
203. C2×#102C2×D3semidirect
204. C2×#102C2×D3semidirect
207. C2×C22⋊C8C2×D3semidirect
215. #380C2×D3semidirect
504. C3×D4#123semidirect
819. D4#883semidirect
936. C3#24032semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#672
C2×#47742
C2×D3×#1022
#739112
C3×#17862
#721282
#702112
#702022
#701982
#701772
#701682
#701672
#699572
#699342
#695232
#240323