Finite Group Databasebeta

← #10827616

Subgroups — #10827616

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×#5513C211yesmaximal, characteristic, complemented
2#82640C211yesmaximal, characteristic
3C2×#4776C211yesmaximal, characteristic, complemented
4C2×#4770C211yesmaximal, characteristic, complemented
5C3×#1874C211yesmaximal, characteristic, complemented
6#71685C211yesmaximal, characteristic, complemented
7#71560C211yesmaximal, characteristic, complemented
8#70213C211yesmaximal, characteristic, complemented
9#70164C211yesmaximal, characteristic, complemented
10#69962C211yesmaximal, characteristic, complemented
11#69958C211yesmaximal, characteristic, complemented
12#68909C211yesmaximal, characteristic, complemented
13#68899C211yesmaximal, characteristic, complemented
14#68884C211yesmaximal, characteristic, complemented
15#68813C211yesmaximal, characteristic, complemented
16#23982—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic, complemented
20C2×#937—21no—
21C22×#214C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#929—21no—
24C2×C4×#67C2211yescharacteristic
25C2×#926—21no—
26C2×#924C2211yescharacteristic, complemented
27C22×#204C2211yescharacteristic
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29#5513—24no—
30#5513—24no—
31C2×#898—21no—
32C2×#897C2211yescharacteristic
33C2×#892C2211yescharacteristic
34C2×#890C2211yescharacteristic, complemented
35C2×#889—21no—
36C2×#887C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40#5223—21no—
41#5221C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#830C2211yescharacteristic, complemented
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic, complemented
47#4988C2211yescharacteristic
48#4987C2211yescharacteristic
49C2×#810C2211yescharacteristic, complemented
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4959—21no—
53#4955—21no—
54#4776—24no—
55#4770—24no—
56C3×#340C2211yescharacteristic, complemented
57C3×#340C2211yescharacteristic, 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#2000—31no—
72#1894—31no—
73#1880—31no—
74#1880—31no—
75#1874—31no—
76#1874D311yescharacteristic, complemented
77#1870—31no—
78#1825—31no—
79C24×D3—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C22×#67D411yescharacteristic
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—41no—
92C2×D3×D4—41no—
93C22×D12C2311yescharacteristic
94C22×C4×D3C2311yescharacteristic
95C22×Dic6C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#121—22no—
99C3×#121—41no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217D411yescharacteristic
111#937—44no—
112C2×#214—22no—
113C2×#214—22no—
114C2×#214—41no—
115#930—22no—
116#930—41no—
117#929—28no—
118C4×#67—22no—
119C4×#67—22no—
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)⋊C4D411yescharacteristic
127#926—28no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132#924—22no—
133#924—22no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4D411yescharacteristic
138C2×C4×Dic3—21no—
139C2×C4×Dic3—21no—
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×#204—22no—
144C2×#204—22no—
145C2×#204—41no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)—41no—
148C2×ΓL(1,𝔽25)—41no—
149#898—28no—
150#897—22no—
151#897D414yescomplemented
152#892—22no—
153#892D414yescomplemented
154#890—22no—
155#890—22no—
156#889—28no—
157#887—22no—
158#887—22no—
159C3×#102—22no—
160C3×#102—22no—
161C3×C22⋊C8—41no—
162#832—22no—
163C3⋊#95—21no—
164#830—41no—
165#821—22no—
166(C2×D3)⋊C8—22no—
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#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×#121C2×D311yescharacteristic
185C2×#120—61no—
186C2×C4×Q8—31no—
187C2×C4×D4—31no—
188C2×#117—31no—
189C2×#117—61no—
190C22×C4⋊C4C2×D311yescharacteristic, complemented
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⋊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#340C2×D311yescharacteristic, complemented
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×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—81no—
237C2×C3×D4#4112yes—
238C22×C3×C4—24no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—42no—
249C22×C3×C4—42no—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2411yescharacteristic
252C2×#67—22no—
253C2×#67—22no—
254C2×#67—41no—
255C2×#67—42no—
256C2×#67—42no—
257C2×#67—42no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—81no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3C2×D411yescharacteristic
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267D3×D4—28no—
268D3×D4—44no—
269D3×D4—44no—
270D3×D4—44no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12#4112yes—
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—
303#217—24no—
304#217—22no—
305#217—42no—
306#217—81no—
307#214—44no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—22no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—42no—
314(C2×D3)⋊C4—81no—
315C4⋊Dic3—24no—
316C4⋊Dic3—21no—
317C4⋊Dic3—24no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3C2×D412yes—
321Dic3⋊C4—24no—
322Dic3⋊C4—24no—
323Dic3⋊C4—24no—
324Dic3⋊C4—22no—
325C4×Dic3—24no—
326C4×Dic3—21no—
327C4×Dic3—21no—
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—31no—
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—21no—
352C23×C4—31no—
353C23×C4C22×D311yescharacteristic
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
367#126—68no—
368#125—62no—
369#125—68no—
370#125—62no—
371#123—68no—
372C22⋊Q8—34no—
373C22⋊Q8—62no—
374C22⋊Q8—62no—
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—62no—
387#117—68no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
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⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—31no—
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×C22⋊C4—61no—
414C2×C42—31no—
415C2×C42—61no—
416C2×C42—61no—
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—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×D4—22no—
466C3×D4—22no—
467C3×D4—41no—
468C3×D4—41no—
469C3×D4—84no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—48no—
476C2×C3×C4—41no—
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×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4C22×D411yescharacteristic
489C2×C3×C4C2×#4111yescharacteristic
490C2×C3×C4C2×#4111yescharacteristic
491C2×C3×C4H(5,𝔽2)11yescharacteristic
492C2×C3×C4H(5,𝔽2)11yescharacteristic
493#67—48no—
494#67—44no—
495#67—84no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3#12012yes—
514D12—22no—
515D12—22no—
516D12—41no—
517D12—41no—
518C4×D3—22no—
519C4×D3—22no—
520C4×D3—22no—
521C4×D3—22no—
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—61no—
533C24—122no—
534C24—122no—
535C24—122no—
536C24—122no—
537C24—122no—
538C24—241no—
539C24—241no—
540C24D3×D411yescharacteristic
541C2×Q8—32no—
542C2×Q8—61no—
543C2×Q8—61no—
544C2×Q8—61no—
545C2×Q8—61no—
546C2×Q8—61no—
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#23512yes—
575C22×C4—24no—
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—21no—
585C22×C4—31no—
586C22×C4—32no—
587C22×C4—32no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
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—64no—
627C4⋊C4—64no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4D3×D412yes—
632C4⋊C4D3×D412yes—
633C22⋊C4—42no—
634C22⋊C4—62no—
635C22⋊C4—64no—
636C22⋊C4—64no—
637C22⋊C4—62no—
638C22⋊C4—64no—
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—42no—
695Dic3—41no—
696Dic3—41no—
697Dic3—42no—
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#91112yes—
734C23C2×D3×D411yescharacteristic
735Q8—62no—
736Q8—62no—
737Q8—121no—
738Q8—121no—
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—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—32no—
757C2×C4—48no—
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—41no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—61no—
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—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—
840C22#549011yescharacteristic
841C22D3×#12011yescharacteristic
842C22#565411yescharacteristic
843C22C2×#91111yescharacteristic
844C22#576211yescharacteristic
845C22#577311yescharacteristic
846C22#577811yescharacteristic
847C4—42no—
848C4—42no—
849C4—41no—
850C4—62no—
851C4—81no—
852C4—121no—
853C4—122no—
854C4—121no—
855C4—122no—
856C4—241no—
857C4#554711yescharacteristic
858C4#555011yescharacteristic
859C4#560711yescharacteristic
860C4#561211yescharacteristic
861C3#2398211yescharacteristic, complemented, Sylow
862C2—42no—
863C2—82no—
864C2—122no—
865C2—242no—
866C2#7488611yescharacteristic
867C2#7876211yescharacteristic
868C2#7890311yescharacteristic
869C2#8000311yescharacteristic
870C2#8004111yescharacteristic
871C2#8130311yescharacteristic
872C2#8133311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1874C2
socleC23×C3C22×D4
prime radical#82640C2
hypercenter#1874D3
hypocenterC3#23982
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#5513C2semidirect
3. C2×#4776C2semidirect
4. C2×#4770C2semidirect
5. C3×#1874C2semidirect
6. #71685C2semidirect
7. #71560C2semidirect
8. #70213C2semidirect
9. #70164C2semidirect
10. #69962C2semidirect
11. #69958C2semidirect
12. #68909C2semidirect
13. #68899C2semidirect
14. #68884C2semidirect
15. #68813C2semidirect
19. C22×C3×C4⋊C4C22semidirect
26. C2×#924C22semidirect
34. C2×#890C22semidirect
36. C2×#887C22semidirect
39. C2×C3×C22⋊C8C22semidirect
43. C2×#830C22semidirect
46. C2×#816C22semidirect
49. C2×#810C22semidirect
56. C3×#340C22semidirect
57. C3×#340C22semidirect
58. #4551C22semidirect
59. #4550C22semidirect
60. #4550C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4529C22semidirect
76. #1874D3semidirect
151. #897D4semidirect
153. #892D4semidirect
190. C22×C4⋊C4C2×D3semidirect
203. C2×C22⋊C8C2×D3semidirect
214. #340C2×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×#55132
#826402
C2×#47762
C2×#47702
C3×#18742
#716852
#715602
#702132
#701642
#699622
#699582
#689092
#688992
#688842
#688132
#239823