Finite Group Databasebeta

← #10827607

Subgroups — #10827607

Order 768.

1424 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5642C211yesmaximal, characteristic, complemented
2C2×#5169C211yesmaximal, characteristic, complemented
3#82640C211yesmaximal, characteristic
4C2×#4770C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic, complemented
6#72048C211yesmaximal, characteristic, complemented
7#71699C211yesmaximal, characteristic, complemented
8#71677C211yesmaximal, characteristic, complemented
9#70271C211yesmaximal, characteristic, complemented
10#70240C211yesmaximal, characteristic, complemented
11#70164C211yesmaximal, characteristic, complemented
12#69958C211yesmaximal, characteristic, complemented
13#69932C211yesmaximal, characteristic, complemented
14#68899C211yesmaximal, characteristic, complemented
15#68873C211yesmaximal, characteristic, complemented
16#23982—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic, complemented
20C2×C3×#121C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic, complemented
23C22×#215C2211yescharacteristic
24C2×#937—21no—
25C2×#930C2211yescharacteristic
26C2×C4×#67C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic, complemented
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29#5642—24no—
30#5642—24no—
31C2×#898—21no—
32C2×#892C2211yescharacteristic
33C2×#890—21no—
34C2×#890C2211yescharacteristic, complemented
35C2×#886—21no—
36C2×#877—21no—
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40C2×#835C2211yescharacteristic, complemented
41#5223—21no—
42#5221C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45C2×#830C2211yescharacteristic, complemented
46#5169—24no—
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50#4988C2211yescharacteristic
51#4987C2211yescharacteristic
52C2×#809C2211yescharacteristic
53#4959—21no—
54#4955—21no—
55#4770—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×#552—31no—
65C2×#450—31no—
66C2×#418—31no—
67#2408—31no—
68#2025—31no—
69#2025—31no—
70#2000—31no—
71#2000D311yescharacteristic, complemented
72#1894—31no—
73#1880—31no—
74#1880—31no—
75#1874—31no—
76#1874—31no—
77#1870—31no—
78#1825—31no—
79C24×D3—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C22×#67D411yescharacteristic
87C23×Dic3—21no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—41no—
93C2×D3×D4—41no—
94C22×D12C2311yescharacteristic
95C22×C4×D3C2311yescharacteristic
96C2×C3×SD16—22no—
97C2×C3×SD16—22no—
98C2×C3×SD16—41no—
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×C22⋊Q8—22no—
102C3×C22⋊Q8—22no—
103C3×#121—22no—
104C3×#121—41no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217D411yescharacteristic
113#946—22no—
114#946D414yescomplemented
115Q8×Dic3—22no—
116Q8×Dic3—22no—
117C2×#215—22no—
118C2×#215—22no—
119C2×#215—41no—
120#937—44no—
121#930—22no—
122#930—41no—
123C4×#67—22no—
124C4×#67—22no—
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×C4⋊Dic3—21no—
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3—22no—
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×Dic3⋊C4D411yescharacteristic
143C2×C4×Dic3—21no—
144C2×C4×Dic3—21no—
145C2×C4×Dic3C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C2×ΓL(1,𝔽25)—22no—
149C2×ΓL(1,𝔽25)—41no—
150C2×ΓL(1,𝔽25)—41no—
151#898—28no—
152#892—22no—
153#892D414yescomplemented
154#890—28no—
155#890—22no—
156#890—22no—
157#886—28no—
158#877—28no—
159C3×#103—41no—
160C3×#102—22no—
161C3×C22⋊C8—41no—
162#835—41no—
163#832—22no—
164#832—22no—
165C3⋊#95—21no—
166#830—41no—
167#821—22no—
168#821—22no—
169(C2×D3)⋊C8—22no—
170#809—22no—
171C23×D4—31no—
172C22×SD16—31no—
173C22×SD16C2×D311yescharacteristic
174C22×M16—31no—
175#552—64no—
176#552—64no—
177C2×#126—61no—
178C2×#125—31no—
179C2×#125—61no—
180C2×#123—61no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8C2×D311yescharacteristic, complemented
183C2×#121—31no—
184C2×#121C2×D311yescharacteristic
185C2×#120—61no—
186C2×C4×Q8—31no—
187C2×C4×D4—31no—
188C2×#117—31no—
189C2×#117—61no—
190C22×C4⋊C4—31no—
191#450—64no—
192#418—64no—
193C2×#103—31no—
194C2×#103C2×D311yescharacteristic, complemented
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×#102C2×D311yescharacteristic
201C2×C22⋊C8—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8C2×D311yescharacteristic, complemented
204#394—61no—
205#392—61no—
206#390—31no—
207#390—31no—
208#380—31no—
209#379—61no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#340C2×D311yescharacteristic, complemented
216#336—31no—
217#336—31no—
218C24×C3—21no—
219C24×C3C2×D411yescharacteristic
220C23×D3—21no—
221C23×D3—42no—
222C23×D3—42no—
223C23×D3—42no—
224C23×D3—42no—
225C23×D3—42no—
226C23×D3—81no—
227C23×D3—81no—
228C23×D3C2×D411yescharacteristic
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8C2×D412yes—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—81no—
243C2×C3×D4#4112yes—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2411yescharacteristic
255C2×#67—22no—
256C2×#67—22no—
257C2×#67—41no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—81no—
264C22×Dic3—24no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—42no—
269C22×Dic3—42no—
270C22×Dic3C2×D411yescharacteristic
271C22×Dic3C2×D411yescharacteristic
272C22×Dic3C2×D411yescharacteristic
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#4112yes—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3C2×D412yes—
288C2×C4×D3C2×D412yes—
289C3×SD16—44no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C3×C4⋊C4—24no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4C2×D412yes—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—42no—
303#217—22no—
304#217—42no—
305#217—81no—
306#215—44no—
307(C2×D3)⋊C4—24no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—22no—
310(C2×D3)⋊C4—42no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—81no—
314C4⋊Dic3—24no—
315C4⋊Dic3—24no—
316C4⋊Dic3—24no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3C2×D412yes—
322C4⋊Dic3C2×D412yes—
323Dic3⋊C4—24no—
324Dic3⋊C4—24no—
325Dic3⋊C4—22no—
326C4×Dic3—24no—
327C4×Dic3—21no—
328C4×Dic3—21no—
329C4×Dic3—24no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336ΓL(1,𝔽25)—44no—
337C25—61no—
338C22×Q8C22×D311yescharacteristic
339C22×D4—21no—
340C22×D4—31no—
341C22×D4—31no—
342C22×D4—62no—
343C22×D4—62no—
344C22×D4—61no—
345C22×D4—62no—
346C22×D4—62no—
347C22×D4—61no—
348C22×D4—121no—
349C22×D4—121no—
350C22×D4C22×D311yescharacteristic
351C23×C4—31no—
352C23×C4—61no—
353C23×C4C22×D311yescharacteristic
354C2×SD16—22no—
355C2×SD16—22no—
356C2×SD16—41no—
357C2×SD16—62no—
358C2×SD16—62no—
359C2×SD16—121no—
360C2×M16—62no—
361C2×M16—121no—
362C2×M16—121no—
363C22×C8—31no—
364C22×C8—31no—
365C22×C8C22×D311yescharacteristic
366C22×C8C22×D311yescharacteristic
367#126—68no—
368#125—62no—
369#125—68no—
370#125—62no—
371#123—68no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—34no—
375C22⋊Q8—62no—
376#121—22no—
377#121—41no—
378#121—62no—
379#121—121no—
380#120—124no—
381C4×Q8—62no—
382C4×Q8—62no—
383C4×D4—62no—
384C4×D4—62no—
385#117—34no—
386#117—68no—
387#117—62no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C22⋊C4—61no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C42—31no—
415C2×C42—61no—
416C2×C42—61no—
417#103—41no—
418#103—121no—
419#102—22no—
420#102—62no—
421#102—62no—
422#102—62no—
423#102—62no—
424#102—62no—
425C22⋊C8—41no—
426C22⋊C8—62no—
427C22⋊C8—121no—
428#95—61no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—22no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3AGL(1,ℤ/8)12yes—
443C23×C3C22×D411yescharacteristic
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—22no—
451C22×D3—48no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C22×D3—41no—
458C22×D3—84no—
459C22×D3—84no—
460C22×D3—84no—
461C22×D3—84no—
462C22×D3—84no—
463C22×D3—84no—
464C22×D3#12012yes—
465C3×Q8—22no—
466C3×Q8—22no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×D4—22no—
470C3×D4—22no—
471C3×D4—41no—
472C3×D4—41no—
473C3×D4—84no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4C22×D411yescharacteristic
491C2×C3×C4C22×D411yescharacteristic
492C2×C3×C4C2×#4111yescharacteristic
493C2×C3×C4C2×#4111yescharacteristic
494C2×C3×C4H(5,𝔽2)11yescharacteristic
495C2×C3×C4H(5,𝔽2)11yescharacteristic
496#67—48no—
497#67—44no—
498#67—84no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—22no—
503C2×Dic3—21no—
504C2×Dic3—22no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—48no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3#12012yes—
518D12—22no—
519D12—22no—
520D12—41no—
521D12—41no—
522C4×D3—22no—
523C4×D3—22no—
524C4×D3—22no—
525C4×D3—22no—
526C3×C8—41no—
527C3×C8—41no—
528C3⋊C8—41no—
529C3⋊C8—41no—
530C24—21no—
531C24—31no—
532C24—61no—
533C24—122no—
534C24—122no—
535C24—122no—
536C24—122no—
537C24—122no—
538C24—241no—
539C24—241no—
540C24D3×D411yescharacteristic
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8D3×D412yes—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—32no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—68no—
556C2×D4—62no—
557C2×D4—62no—
558C2×D4—61no—
559C2×D4—61no—
560C2×D4—61no—
561C2×D4—61no—
562C2×D4—61no—
563C2×D4—81no—
564C2×D4—122no—
565C2×D4—124no—
566C2×D4—124no—
567C2×D4—124no—
568C2×D4—121no—
569C2×D4—122no—
570C2×D4—122no—
571C2×D4—122no—
572C2×D4—122no—
573C2×D4—241no—
574C2×D4#23712yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—31no—
585C22×C4—32no—
586C22×C4—32no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—64no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—122no—
598C22×C4—122no—
599C22×C4D3×D411yescharacteristic
600C22×C4C23×D311yescharacteristic
601SD16—44no—
602SD16—124no—
603M16—124no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—61no—
611C2×C8—61no—
612C2×C8—61no—
613C2×C8—61no—
614C2×C8—61no—
615C2×C8—61no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—32no—
621C4⋊C4—32no—
622C4⋊C4—62no—
623C4⋊C4—64no—
624C4⋊C4—64no—
625C4⋊C4—64no—
626C4⋊C4—64no—
627C4⋊C4—64no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4D3×D412yes—
633C22⋊C4—24no—
634C22⋊C4—42no—
635C22⋊C4—62no—
636C22⋊C4—64no—
637C22⋊C4—64no—
638C22⋊C4—62no—
639C22⋊C4—122no—
640C22⋊C4—122no—
641C22⋊C4—122no—
642C22⋊C4—122no—
643C22⋊C4—241no—
644C22⋊C4—241no—
645C42—64no—
646C42—64no—
647C42—61no—
648C42—61no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3C2×#12011yescharacteristic
664C22×C3#54611yescharacteristic
665C22×C3#54611yescharacteristic
666C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
667C22×C3#57511yescharacteristic
668C22×C3#57711yescharacteristic
669C22×C3#57711yescharacteristic
670C2×D3—22no—
671C2×D3—22no—
672C2×D3—22no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—42no—
678C2×D3—42no—
679C2×D3—42no—
680C2×D3—816no—
681C2×D3—81no—
682C2×D3—81no—
683C2×D3—81no—
684C2×D3—81no—
685C3×C4—41no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4—81no—
689C3×C4#52511yescharacteristic
690C3×C4#53511yescharacteristic
691C3×C4#54611yescharacteristic
692C3×C4#54611yescharacteristic
693Dic3—22no—
694Dic3—41no—
695Dic3—42no—
696Dic3—42no—
697Dic3—41no—
698Dic3—81no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—32no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—61no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23—61no—
719C23—62no—
720C23—128no—
721C23—121no—
722C23—121no—
723C23—121no—
724C23—121no—
725C23—121no—
726C23—121no—
727C23—244no—
728C23—244no—
729C23—244no—
730C23—244no—
731C23—244no—
732C23—244no—
733C23#91412yes—
734C23C2×D3×D411yescharacteristic
735Q8—22no—
736Q8—22no—
737Q8—41no—
738Q8—41no—
739D4—22no—
740D4—22no—
741D4—41no—
742D4—41no—
743D4—62no—
744D4—62no—
745D4—84no—
746D4—128no—
747D4—124no—
748D4—121no—
749D4—121no—
750D4—244no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—32no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—62no—
780C2×C4—61no—
781C2×C4—62no—
782C2×C4—128no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4C2×D3×D411yescharacteristic
791C2×C4C2×D3×D411yescharacteristic
792C2×C4C2×#23711yescharacteristic
793C2×C4#100411yescharacteristic
794C2×C4#100411yescharacteristic
795C2×C4D3×#4111yescharacteristic
796C8—41no—
797C8—41no—
798C8—121no—
799C8—121no—
800C2×C3—42no—
801C2×C3—82no—
802C2×C3#240411yescharacteristic
803C2×C3#300611yescharacteristic
804C2×C3#301011yescharacteristic
805C2×C3#331011yescharacteristic
806C2×C3#331011yescharacteristic
807C2×C3#332311yescharacteristic
808C2×C3#332311yescharacteristic
809D3—42no—
810D3—82no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—62no—
822C22—62no—
823C22—62no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—122no—
833C22—122no—
834C22—122no—
835C22—2416no—
836C22—241no—
837C22—241no—
838C22—241no—
839C22—241no—
840C22D3×#12011yescharacteristic
841C22#559111yescharacteristic
842C22#561011yescharacteristic
843C22C2×#91411yescharacteristic
844C22#577011yescharacteristic
845C22#577511yescharacteristic
846C22#577711yescharacteristic
847C4—41no—
848C4—42no—
849C4—42no—
850C4—62no—
851C4—81no—
852C4—121no—
853C4—122no—
854C4—122no—
855C4—121no—
856C4—241no—
857C4#559111yescharacteristic
858C4#560611yescharacteristic
859C4#561011yescharacteristic
860C4#571511yescharacteristic
861C3#2398211yescharacteristic, complemented, Sylow
862C2—42no—
863C2—82no—
864C2—122no—
865C2—242no—
866C2#7675411yescharacteristic
867C2#8004011yescharacteristic
868C2#8008611yescharacteristic
869C2#8016011yescharacteristic
870C2#8025811yescharacteristic
871C2#8068511yescharacteristic
872C2#8082711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radical#82640C2
hypercenter#2000D3
hypocenterC3#23982
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5642C2semidirect
2. C2×#5169C2semidirect
4. C2×#4770C2semidirect
5. C3×#2000C2semidirect
6. #72048C2semidirect
7. #71699C2semidirect
8. #71677C2semidirect
9. #70271C2semidirect
10. #70240C2semidirect
11. #70164C2semidirect
12. #69958C2semidirect
13. #69932C2semidirect
14. #68899C2semidirect
15. #68873C2semidirect
19. C2×C3×C22⋊Q8C22semidirect
22. C2×Q8×Dic3C22semidirect
27. C22×C4⋊Dic3C22semidirect
34. C2×#890C22semidirect
37. C2×C3×#103C22semidirect
39. C2×C3×C22⋊C8C22semidirect
40. C2×#835C22semidirect
45. C2×#830C22semidirect
56. C3×#340C22semidirect
57. #4551C22semidirect
58. #4551C22semidirect
59. #4550C22semidirect
60. #4550C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4529C22semidirect
71. #2000D3semidirect
114. #946D4semidirect
153. #892D4semidirect
182. C2×C22⋊Q8C2×D3semidirect
194. C2×#103C2×D3semidirect
203. C2×C22⋊C8C2×D3semidirect
215. #340C2×D3semidirect
861. C3#23982semidirect

Maximal subgroups

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

subgroupindex
C2×#56422
C2×#51692
#826402
C2×#47702
C3×#20002
#720482
#716992
#716772
#702712
#702402
#701642
#699582
#699322
#688992
#688732
#239823