Finite Group Databasebeta

← #10827610

Subgroups — #10827610

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×#5581C211yesmaximal, characteristic, complemented
2C2×#5169C211yesmaximal, characteristic, complemented
3C2×#4770C211yesmaximal, characteristic, complemented
4#76436C211yesmaximal, characteristic
5C3×#1880C211yesmaximal, characteristic, complemented
6#72054C211yesmaximal, characteristic, complemented
7#71633C211yesmaximal, characteristic, complemented
8#70272C211yesmaximal, characteristic, complemented
9#70271C211yesmaximal, characteristic, complemented
10#70200C211yesmaximal, characteristic, complemented
11#69639C211yesmaximal, characteristic, complemented
12#68880C211yesmaximal, characteristic, complemented
13#68813C211yesmaximal, characteristic, complemented
14#68679C211yesmaximal, characteristic, complemented
15#68669C211yesmaximal, characteristic, complemented
16#23982—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic, complemented
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic, complemented
22C22×#215C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C22×ΓL(1,𝔽25)C2211yescharacteristic
25#5581—24no—
26#5581—24no—
27C2×#895C2211yescharacteristic
28C2×#894—21no—
29C2×#892C2211yescharacteristic
30C2×D3×C4⋊C4C2211yescharacteristic, complemented
31C2×#889—21no—
32C2×#882—21no—
33C2×#876—21no—
34C2×C4×D12C2211yescharacteristic
35C2×#872—21no—
36C2×#870C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C2×#835C2211yescharacteristic, complemented
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5169—24no—
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
48C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
49#4987C2211yescharacteristic
50C2×#809C2211yescharacteristic
51#4961—21no—
52#4960—21no—
53#4955—21no—
54#4939C2211yescharacteristic
55#4770—24no—
56C3×#340C2211yescharacteristic, complemented
57C3×#336C2211yescharacteristic, complemented
58#4551C2211yescharacteristic, complemented
59#4551C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4524C2211yescharacteristic, complemented
64C2×#552—31no—
65C2×#450—31no—
66C2×#418—31no—
67#2408—31no—
68#2025—31no—
69#2025—31no—
70#2000—31no—
71#2000—31no—
72#1894—31no—
73#1880—31no—
74#1880D311yescharacteristic, complemented
75#1874—31no—
76#1874—31no—
77#1870—31no—
78#1825—31no—
79C24×D3—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C2×D3×D4—22no—
85C2×D3×D4—22no—
86C2×D3×D4—22no—
87C2×D3×D4—22no—
88C2×D3×D4—41no—
89C2×D3×D4—41no—
90C22×D12—21no—
91C22×D12D411yescharacteristic
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×C4×D3C2311yescharacteristic
95C22×C4×D3C2311yescharacteristic
96C2×C3×SD16—22no—
97C2×C3×SD16—22no—
98C2×C3×SD16—41no—
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×C4×Q8—22no—
102C3×C4×Q8—22no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C42—21no—
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111#946—22no—
112#946—22no—
113#946—22no—
114#946D414yescomplemented
115C2×#215—22no—
116C2×#215—22no—
117C2×#215—41no—
118#938—22no—
119#938—41no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
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)⋊C4D411yescharacteristic
128C2×(C2×D3)⋊C4D411yescharacteristic
129C2×C4⋊Dic3D411yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×C4×Dic3—21no—
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)—41no—
143C2×ΓL(1,𝔽25)—41no—
144#895—22no—
145#895—41no—
146#894—28no—
147#892—22no—
148#892D414yescomplemented
149D3×C4⋊C4—22no—
150D3×C4⋊C4—22no—
151#889—28no—
152#882—44no—
153#876—28no—
154C4×D12—22no—
155C4×D12—22no—
156#872—28no—
157#870—22no—
158#870—22no—
159C3×#103—41no—
160C3×#102—22no—
161#835—41no—
162#832—22no—
163#832—22no—
164C3⋊#95—21no—
165#821—22no—
166#821—22no—
167(C2×D3)⋊C8—22no—
168(C2×D3)⋊C8—41no—
169(C2×D3)⋊C8—41no—
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⋊Q8—31no—
183C2×#121—31no—
184C2×#121—31no—
185C2×#120—61no—
186C2×C4×Q8C2×D311yescharacteristic, complemented
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⋊C8—31no—
204#394—61no—
205#392—61no—
206#390—31no—
207#390C2×D311yescharacteristic
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#336C2×D311yescharacteristic, complemented
218C24×C3—21no—
219C23×D3—21no—
220C23×D3—42no—
221C23×D3—42no—
222C23×D3—42no—
223C23×D3—42no—
224C23×D3—42no—
225C23×D3—81no—
226C23×D3—81no—
227C23×D3C2×D411yescharacteristic
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#4112yes—
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×Dic3—21no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258D3×D4—28no—
259D3×D4—44no—
260D3×D4—44no—
261D3×D4—44no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—22no—
267C2×D12—22no—
268C2×D12—21no—
269C2×D12—41no—
270C2×D12—42no—
271C2×D12—42no—
272C2×D12—81no—
273C2×D12#4112yes—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—24no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—42no—
286C2×C4×D3—42no—
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—42no—
302C3×C22⋊C4—81no—
303C3×C42—24no—
304C3×C42—21no—
305C3×C42—21no—
306#217—42no—
307#215—44no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—22no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4—42no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—42no—
316(C2×D3)⋊C4—81no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—22no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3C2×D412yes—
323C4⋊Dic3C2×D412yes—
324Dic3⋊C4—24no—
325Dic3⋊C4—24no—
326Dic3⋊C4—24no—
327Dic3⋊C4—24no—
328Dic3⋊C4—24no—
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—31no—
340C22×D4—31no—
341C22×D4—61no—
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—31no—
353C23×C4—61no—
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—62no—
370#125—68no—
371#123—68no—
372C22⋊Q8—34no—
373C22⋊Q8—62no—
374C22⋊Q8—62no—
375C22⋊Q8—62no—
376#121—62no—
377#121—62no—
378#121—121no—
379#121—121no—
380#120—124no—
381C4×Q8—22no—
382C4×Q8—22no—
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—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4—62no—
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—21no—
415C2×C42—61no—
416C2×C42C22×D311yescharacteristic
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—62no—
426C22⋊C8—121no—
427C22⋊C8—121no—
428#95—61no—
429C23×C3—22no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3C22×D411yescharacteristic
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—22no—
450C22×D3—48no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C22×D3—84no—
458C22×D3—84no—
459C22×D3—84no—
460C22×D3—84no—
461C22×D3—84no—
462C22×D3—84no—
463C22×D3#12012yes—
464C22×D3AGL(1,ℤ/8)12yes—
465C3×Q8—22no—
466C3×Q8—22no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×D4—22no—
470C3×D4—22no—
471C3×D4—41no—
472C3×D4—41no—
473C2×C3×C4—22no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
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×C4C22×D411yescharacteristic
489C2×C3×C4C22×D411yescharacteristic
490C2×C3×C4C2×#4111yescharacteristic
491C2×C3×C4C2×#4111yescharacteristic
492C2×C3×C4H(5,𝔽2)11yescharacteristic
493C2×C3×C4H(5,𝔽2)11yescharacteristic
494#67—48no—
495#67—84no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—22no—
499C2×Dic3—21no—
500C2×Dic3—22no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3#12012yes—
511D12—22no—
512D12—22no—
513D12—44no—
514D12—41no—
515D12—41no—
516D12—84no—
517C4×D3—22no—
518C4×D3—22no—
519C4×D3—22no—
520C4×D3—22no—
521C4×D3—48no—
522C4×D3—41no—
523C4×D3—41no—
524C4×D3—41no—
525C4×D3—41no—
526C3×C8—41no—
527C3×C8—41no—
528C3⋊C8—41no—
529C3⋊C8—41no—
530C24—21no—
531C24—31no—
532C24—31no—
533C24—61no—
534C24—122no—
535C24—122no—
536C24—122no—
537C24—122no—
538C24—122no—
539C24—241no—
540C24—241no—
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—62no—
554C2×D4—62no—
555C2×D4—68no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—61no—
560C2×D4—61no—
561C2×D4—121no—
562C2×D4—122no—
563C2×D4—122no—
564C2×D4—122no—
565C2×D4—124no—
566C2×D4—124no—
567C2×D4—124no—
568C2×D4—122no—
569C2×D4—122no—
570C2×D4—122no—
571C2×D4—122no—
572C2×D4—241no—
573C2×D4—241no—
574C2×D4#23512yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—31no—
579C22×C4—32no—
580C22×C4—32no—
581C22×C4—31no—
582C22×C4—64no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—122no—
597C22×C4—122no—
598C22×C4D3×D411yescharacteristic
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—42no—
634C22⋊C4—62no—
635C22⋊C4—62no—
636C22⋊C4—64no—
637C22⋊C4—64no—
638C22⋊C4—64no—
639C22⋊C4—81no—
640C22⋊C4—122no—
641C22⋊C4—122no—
642C22⋊C4—122no—
643C22⋊C4—122no—
644C22⋊C4—241no—
645C42—24no—
646C42—21no—
647C42—21no—
648C42—64no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3C2×#12011yescharacteristic
657C22×C3#54611yescharacteristic
658C22×C3#54611yescharacteristic
659C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
660C22×C3#57511yescharacteristic
661C22×C3#57711yescharacteristic
662C22×C3#57711yescharacteristic
663C2×D3—22no—
664C2×D3—22no—
665C2×D3—22no—
666C2×D3—22no—
667C2×D3—22no—
668C2×D3—22no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
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—42no—
686C3×C4—42no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—81no—
690C3×C4#52511yescharacteristic
691C3×C4#53511yescharacteristic
692C3×C4#54611yescharacteristic
693C3×C4#54611yescharacteristic
694Dic3—22no—
695Dic3—41no—
696Dic3—42no—
697Dic3—42no—
698Dic3—81no—
699C23—22no—
700C23—32no—
701C23—32no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—61no—
709C23—61no—
710C23—61no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23—61no—
719C23—61no—
720C23—62no—
721C23—128no—
722C23—121no—
723C23—121no—
724C23—121no—
725C23—121no—
726C23—121no—
727C23—121no—
728C23—244no—
729C23—244no—
730C23—244no—
731C23—244no—
732C23—244no—
733C23—244no—
734C23C2×D3×D411yescharacteristic
735Q8—22no—
736Q8—22no—
737Q8—41no—
738Q8—41no—
739D4—22no—
740D4—22no—
741D4—41no—
742D4—41no—
743D4—62no—
744D4—62no—
745D4—124no—
746D4—128no—
747D4—121no—
748D4—121no—
749D4—244no—
750D4—244no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—32no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—61no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—128no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4C2×#23511yescharacteristic
791C2×C4C2×D3×D411yescharacteristic
792C2×C4C2×D3×D411yescharacteristic
793C2×C4#100411yescharacteristic
794C2×C4D3×#4111yescharacteristic
795C2×C4#100911yescharacteristic
796C8—41no—
797C8—41no—
798C8—121no—
799C8—121no—
800C2×C3—82no—
801C2×C3#240411yescharacteristic
802C2×C3#300611yescharacteristic
803C2×C3#301011yescharacteristic
804C2×C3#331011yescharacteristic
805C2×C3#331011yescharacteristic
806C2×C3#332311yescharacteristic
807C2×C3#332311yescharacteristic
808D3—42no—
809D3—42no—
810D3—82no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—62no—
815C22—62no—
816C22—62no—
817C22—62no—
818C22—62no—
819C22—62no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—122no—
833C22—122no—
834C22—122no—
835C22—2416no—
836C22—241no—
837C22—241no—
838C22—241no—
839C22—241no—
840C22#555011yescharacteristic
841C22D3×#12011yescharacteristic
842C22#561211yescharacteristic
843C22#576211yescharacteristic
844C22#576811yescharacteristic
845C22D3×AGL(1,ℤ/8)11yescharacteristic
846C22#577811yescharacteristic
847C4—42no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—62no—
852C4—81no—
853C4—121no—
854C4—122no—
855C4—122no—
856C4—241no—
857C4#549011yescharacteristic
858C4#554711yescharacteristic
859C4#560711yescharacteristic
860C4#565411yescharacteristic
861C3#2398211yescharacteristic, complemented, Sylow
862C2—82no—
863C2—122no—
864C2—122no—
865C2—242no—
866C2#7488611yescharacteristic
867C2#7968211yescharacteristic
868C2#7980011yescharacteristic
869C2#8004111yescharacteristic
870C2#8008411yescharacteristic
871C2#8039711yescharacteristic
872C2#8062111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1880C2
socleC23×C3C22×D4
prime radical#76436C2
hypercenter#1880D3
hypocenterC3#23982
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×#5581C2semidirect
2. C2×#5169C2semidirect
3. C2×#4770C2semidirect
5. C3×#1880C2semidirect
6. #72054C2semidirect
7. #71633C2semidirect
8. #70272C2semidirect
9. #70271C2semidirect
10. #70200C2semidirect
11. #69639C2semidirect
12. #68880C2semidirect
13. #68813C2semidirect
14. #68679C2semidirect
15. #68669C2semidirect
19. C2×C3×C4×Q8C22semidirect
21. C2×#946C22semidirect
30. C2×D3×C4⋊C4C22semidirect
36. C2×#870C22semidirect
37. C2×C3×#103C22semidirect
40. C2×#835C22semidirect
47. C2×(C2×D3)⋊C8C22semidirect
48. C2×(C2×D3)⋊C8C22semidirect
56. C3×#340C22semidirect
57. C3×#336C22semidirect
58. #4551C22semidirect
59. #4551C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4524C22semidirect
74. #1880D3semidirect
114. #946D4semidirect
148. #892D4semidirect
186. C2×C4×Q8C2×D3semidirect
194. C2×#103C2×D3semidirect
215. #340C2×D3semidirect
217. #336C2×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×#55812
C2×#51692
C2×#47702
#764362
C3×#18802
#720542
#716332
#702722
#702712
#702002
#696392
#688802
#688132
#686792
#686692
#239823