Finite Group Databasebeta

← #10827576

Subgroups — #10827576

Order 768.

1418 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×#5732C211yesmaximal, characteristic, complemented
2C2×#4776C211yesmaximal, characteristic, complemented
3C2×#4770C211yesmaximal, characteristic, complemented
4#76436C211yesmaximal, characteristic
5C3×#2023C211yesmaximal, characteristic, complemented
6#71792C211yesmaximal, characteristic, complemented
7#70205C211yesmaximal, characteristic, complemented
8#70201C211yesmaximal, characteristic, complemented
9#69660C211yesmaximal, characteristic, complemented
10#68887C211yesmaximal, characteristic, complemented
11#68884C211yesmaximal, characteristic, complemented
12#68881C211yesmaximal, characteristic, complemented
13#68813C211yesmaximal, characteristic, complemented
14#68686C211yesmaximal, characteristic, complemented
15#68669C211yesmaximal, characteristic, complemented
16#23979—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic, complemented
19C2×#947—21no—
20C2×Q8×Dic3—21no—
21C2×#938C2211yescharacteristic
22C22×#214C2211yescharacteristic
23C22×#204C2211yescharacteristic
24C22×ΓL(1,𝔽25)C2211yescharacteristic
25#5732—24no—
26#5732—24no—
27C2×#898—21no—
28C2×#898—21no—
29C2×#897C2211yescharacteristic
30C2×#897C2211yescharacteristic, complemented
31C2×#895C2211yescharacteristic
32C2×#892C2211yescharacteristic
33C2×#892C2211yescharacteristic, complemented
34C2×#882—21no—
35C2×C4×D12C2211yescharacteristic
36C2×C4×Dic6C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
44C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
45C2×#816C2211yescharacteristic, complemented
46#4987C2211yescharacteristic
47C2×#810C2211yescharacteristic, complemented
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50#4961—21no—
51#4960—21no—
52#4955—21no—
53#4939C2211yescharacteristic
54#4776—24no—
55#4770—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×#556—31no—
65C2×#450—31no—
66C2×#418—31no—
67#2408—31no—
68#2023—31no—
69#2023D311yescharacteristic, complemented
70#2000—31no—
71#2000—31no—
72#1894—31no—
73#1880—31no—
74#1880—31no—
75#1875—31no—
76#1875—31no—
77#1870—31no—
78#1825—31no—
79C24×D3—21no—
80C22×C3×Q8—21no—
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×D3C2311yescharacteristic
94C22×C4×D3C2311yescharacteristic
95C22×Dic6C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×C4⋊Q8—22no—
99C3×C4⋊Q8—22no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C42C2311yescharacteristic
107C2×#217—21no—
108#947—28no—
109Q8×Dic3—28no—
110#938—22no—
111#938—41no—
112C2×#214—22no—
113C2×#214—22no—
114C2×#214—41no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×(C2×D3)⋊C4D411yescharacteristic
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3D411yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3—21no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3—21no—
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C2×#204—22no—
137C2×#204—22no—
138C2×#204—41no—
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)—41no—
141C2×ΓL(1,𝔽25)—41no—
142#898—28no—
143#898—28no—
144#897—22no—
145#897—22no—
146#897—22no—
147#897D414yescomplemented
148#895—22no—
149#895—41no—
150#892—22no—
151#892—22no—
152#892—22no—
153#892D414yescomplemented
154#882—44no—
155C4×D12—22no—
156C4×D12—22no—
157C4×Dic6—22no—
158C4×Dic6—22no—
159C3×#102—22no—
160C3×#102—22no—
161#832—22no—
162C3⋊#95—21no—
163#821—22no—
164(C2×D3)⋊C8—22no—
165(C2×D3)⋊C8—41no—
166(C2×D3)⋊C8—41no—
167#816—41no—
168#810—41no—
169#809—22no—
170#809—22no—
171C23×D4—31no—
172C22×SD16—31no—
173C22×SD16—31no—
174C22×M16—31no—
175#556—64no—
176#556—64no—
177C2×C4⋊Q8C2×D311yescharacteristic, complemented
178C2×#126—61no—
179C2×#126—61no—
180C2×#124—61no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×#121—31no—
184C2×#121—31no—
185C2×#120—61no—
186C2×C4×Q8—31no—
187C2×C4×Q8—61no—
188C2×C4×D4—31no—
189C2×#117—31no—
190C2×#117—31no—
191#450—64no—
192#418—64no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102C2×D311yescharacteristic
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#340C2×D311yescharacteristic, complemented
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—24no—
230C2×C3×Q8—42no—
231C2×C3×Q8—42no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4#4112yes—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—81no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255D3×D4—28no—
256D3×D4—44no—
257D3×D4—44no—
258D3×D4—44no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—22no—
264C2×D12—22no—
265C2×D12—21no—
266C2×D12—41no—
267C2×D12—42no—
268C2×D12—42no—
269C2×D12—81no—
270C2×D12#4112yes—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3C2×D412yes—
282C2×C4×D3C2×D412yes—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6C2×D412yes—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4C2×D412yes—
301C3×C4⋊C4C2×D412yes—
302C3×C22⋊C4—42no—
303C3×C22⋊C4—81no—
304C3×C42—21no—
305C3×C42—21no—
306#217—42no—
307#214—44no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—22no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—22no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—42no—
316(C2×D3)⋊C4—42no—
317(C2×D3)⋊C4—81no—
318C4⋊Dic3—24no—
319C4⋊Dic3—21no—
320C4⋊Dic3—22no—
321C4⋊Dic3—24no—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3C2×D412yes—
325Dic3⋊C4—24no—
326C4×Dic3—24no—
327C4×Dic3—24no—
328C4×Dic3—24no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335#204—44no—
336ΓL(1,𝔽25)—44no—
337C25—61no—
338C22×Q8—21no—
339C22×Q8—31no—
340C22×D4—31no—
341C22×D4—31no—
342C22×D4—61no—
343C22×D4—62no—
344C22×D4—62no—
345C22×D4—61no—
346C22×D4—62no—
347C22×D4—62no—
348C22×D4—61no—
349C22×D4—121no—
350C22×D4—121no—
351C22×D4C22×D311yescharacteristic
352C23×C4—31no—
353C23×C4—31no—
354C2×SD16—62no—
355C2×SD16—62no—
356C2×SD16—62no—
357C2×SD16—62no—
358C2×SD16—121no—
359C2×SD16—121no—
360C2×M16—62no—
361C2×M16—121no—
362C2×M16—121no—
363C22×C8—31no—
364C22×C8—31no—
365C22×C8C22×D311yescharacteristic
366C22×C8C22×D311yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369#126—68no—
370#126—68no—
371#124—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—62no—
382C4×Q8—62no—
383C4×Q8—68no—
384C4×D4—62no—
385C4×D4—62no—
386#117—34no—
387#117—62no—
388#117—62no—
389#117—62no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—31no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
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×C42—61no—
414C2×C42—61no—
415C2×C42—61no—
416C2×C42C22×D311yescharacteristic
417#103—121no—
418#103—121no—
419#102—22no—
420#102—22no—
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—22no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—21no—
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—48no—
466C3×D4—22no—
467C3×D4—22no—
468C3×D4—41no—
469C3×D4—41no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4AGL(1,ℤ/8)12yes—
485C2×C3×C4C22×D411yescharacteristic
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4C2×#4111yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×C3×C4H(5,𝔽2)11yescharacteristic
490C2×C3×C4H(5,𝔽2)11yescharacteristic
491#67—48no—
492#67—84no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—22no—
496C2×Dic3—21no—
497C2×Dic3—22no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3#12012yes—
508D12—22no—
509D12—22no—
510D12—44no—
511D12—41no—
512D12—41no—
513D12—84no—
514C4×D3—22no—
515C4×D3—22no—
516C4×D3—22no—
517C4×D3—22no—
518C4×D3—41no—
519C4×D3—41no—
520C4×D3—41no—
521C4×D3—41no—
522Dic6—22no—
523Dic6—22no—
524Dic6—41no—
525Dic6—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—24no—
542C2×Q8—32no—
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—61no—
546C2×Q8—61no—
547C2×Q8—61no—
548C2×Q8—61no—
549C2×Q8—61no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—32no—
556C2×D4—62no—
557C2×D4—68no—
558C2×D4—62no—
559C2×D4—61no—
560C2×D4—61no—
561C2×D4—61no—
562C2×D4—61no—
563C2×D4—61no—
564C2×D4—121no—
565C2×D4—122no—
566C2×D4—122no—
567C2×D4—122no—
568C2×D4—124no—
569C2×D4—124no—
570C2×D4—124no—
571C2×D4—122no—
572C2×D4—122no—
573C2×D4—122no—
574C2×D4—122no—
575C2×D4—241no—
576C2×D4—241no—
577C2×D4#23912yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—31no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—31no—
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—61no—
597C22×C4—61no—
598C22×C4D3×D411yescharacteristic
599C22×C4D3×D411yescharacteristic
600C22×C4C23×D311yescharacteristic
601SD16—124no—
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—21no—
621C4⋊C4—32no—
622C4⋊C4—62no—
623C4⋊C4—64no—
624C4⋊C4—64no—
625C4⋊C4—64no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4D3×D412yes—
630C4⋊C4D3×D412yes—
631C22⋊C4—42no—
632C22⋊C4—62no—
633C22⋊C4—62no—
634C22⋊C4—64no—
635C22⋊C4—64no—
636C22⋊C4—64no—
637C22⋊C4—64no—
638C22⋊C4—81no—
639C22⋊C4—122no—
640C22⋊C4—122no—
641C22⋊C4—122no—
642C22⋊C4—122no—
643C22⋊C4—241no—
644C42—21no—
645C42—21no—
646C42—64no—
647C42—64no—
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—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—42no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—42no—
677C2×D3—41no—
678C2×D3—42no—
679C2×D3—41no—
680C2×D3—816no—
681C2×D3—81no—
682C2×D3—81no—
683C2×D3—81no—
684C2×D3—81no—
685C3×C4—22no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4—41no—
689C3×C4—81no—
690C3×C4#52511yescharacteristic
691C3×C4#53511yescharacteristic
692C3×C4#54611yescharacteristic
693C3×C4#54611yescharacteristic
694Dic3—22no—
695Dic3—42no—
696Dic3—41no—
697Dic3—42no—
698Dic3—81no—
699C23—22no—
700C23—32no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—61no—
708C23—61no—
709C23—61no—
710C23—61no—
711C23—61no—
712C23—61no—
713C23—62no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23—61no—
719C23—61no—
720C23—61no—
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—48no—
736Q8—62no—
737Q8—62no—
738Q8—121no—
739Q8—121no—
740D4—22no—
741D4—22no—
742D4—41no—
743D4—41no—
744D4—62no—
745D4—62no—
746D4—124no—
747D4—128no—
748D4—121no—
749D4—121no—
750D4—244no—
751D4—244no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
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—61no—
776C2×C4—62no—
777C2×C4—61no—
778C2×C4—121no—
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#91112yes—
790C2×C4C2×D3×D411yescharacteristic
791C2×C4C2×D3×D411yescharacteristic
792C2×C4C2×#23911yescharacteristic
793C2×C4D3×#4111yescharacteristic
794C2×C4#100911yescharacteristic
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#331111yescharacteristic
805C2×C3#331111yescharacteristic
806C2×C3#332411yescharacteristic
807C2×C3#332411yescharacteristic
808D3—42no—
809D3—81no—
810D3—82no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—62no—
815C22—62no—
816C22—62no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—122no—
827C22—121no—
828C22—122no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—122no—
834C22—121no—
835C22—2416no—
836C22—241no—
837C22—241no—
838C22—241no—
839C22—241no—
840C22D3×#12011yescharacteristic
841C22#563011yescharacteristic
842C22#567611yescharacteristic
843C22C2×#91111yescharacteristic
844C22#576211yescharacteristic
845C22#577311yescharacteristic
846C22#577811yescharacteristic
847C4—22no—
848C4—42no—
849C4—42no—
850C4—41no—
851C4—62no—
852C4—81no—
853C4—121no—
854C4—122no—
855C4—122no—
856C4—241no—
857C4#562711yescharacteristic
858C4#563011yescharacteristic
859C4#567411yescharacteristic
860C4#567611yescharacteristic
861C3#2397911yescharacteristic, complemented, Sylow
862C2—82no—
863C2—122no—
864C2—241no—
865C2—242no—
866C2#7686311yescharacteristic
867C2#8000311yescharacteristic
868C2#8004111yescharacteristic
869C2#8098411yescharacteristic
870C2#8107811yescharacteristic
871C2#8158011yescharacteristic
872C2#8169811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2023C2
socleC23×C3C22×D4
prime radical#76436C2
hypercenter#2023D3
hypocenterC3#23979
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×#5732C2semidirect
2. C2×#4776C2semidirect
3. C2×#4770C2semidirect
5. C3×#2023C2semidirect
6. #71792C2semidirect
7. #70205C2semidirect
8. #70201C2semidirect
9. #69660C2semidirect
10. #68887C2semidirect
11. #68884C2semidirect
12. #68881C2semidirect
13. #68813C2semidirect
14. #68686C2semidirect
15. #68669C2semidirect
18. C2×C3×C4⋊Q8C22semidirect
30. C2×#897C22semidirect
33. C2×#892C22semidirect
36. C2×C4×Dic6C22semidirect
43. C2×(C2×D3)⋊C8C22semidirect
44. C2×(C2×D3)⋊C8C22semidirect
45. C2×#816C22semidirect
47. C2×#810C22semidirect
56. C3×#340C22semidirect
57. C3×#340C22semidirect
58. C3×#336C22semidirect
59. #4551C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4524C22semidirect
69. #2023D3semidirect
147. #897D4semidirect
153. #892D4semidirect
177. C2×C4⋊Q8C2×D3semidirect
214. #340C2×D3semidirect
215. #340C2×D3semidirect
217. #336C2×D3semidirect
861. C3#23979semidirect

Maximal subgroups

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

subgroupindex
C2×#57322
C2×#47762
C2×#47702
#764362
C3×#20232
#717922
#702052
#702012
#696602
#688872
#688842
#688812
#688132
#686862
#686692
#239793