Finite Group Databasebeta

← #10823195

Subgroups — #10823195

Order 768.

1458 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#915C211yesmaximal, characteristic
2C2×#4837C211yesmaximal, characteristic, complemented
3C2×#4802C211yesmaximal, characteristic, complemented
4C2×#4771C211yesmaximal, characteristic
5D3×#391C211yesmaximal, characteristic, complemented
6#76290C211yesmaximal, characteristic
7C3×#2055C211yesmaximal, characteristic, complemented
8#72051C211yesmaximal, characteristic, complemented
9#70487C211yesmaximal, characteristic, complemented
10#70285C211yesmaximal, characteristic, complemented
11#70217C211yesmaximal, characteristic, complemented
12#69681C211yesmaximal, characteristic, complemented
13#69651C211yesmaximal, characteristic, complemented
14#68867C211yesmaximal, characteristic, complemented
15#68864C211yesmaximal, characteristic, complemented
16#23547—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×#237C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#214C2211yescharacteristic
22C2×#915—24no—
23C2×#915—24no—
24C2×#915—24no—
25C22×Dic12C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×ΓL(1,𝔽25)C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×C42×D3C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C3×#391C2211yescharacteristic
35C3×#390C2211yescharacteristic
36#5229C2211yescharacteristic
37C2×#835C2211yescharacteristic
38#5221C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#816C2211yescharacteristic
41C2×#816C2211yescharacteristic
42C2×Dic3⋊C8C2211yescharacteristic
43C2×Dic3⋊C8C2211yescharacteristic
44#4973C2211yescharacteristic
45#4973C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48#4956—21no—
49#4956—21no—
50Dic3×C22⋊C4—21no—
51Dic3×C22⋊C4—21no—
52#4929C2211yescharacteristic
53#4929C2211yescharacteristic
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55#4837—24no—
56#4802—24no—
57#4771—24no—
58D3×#95—21no—
59D3×#95—21no—
60#4646—21no—
61#4646—21no—
62C3×#340C2211yescharacteristic
63#4551C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C22×#137—31no—
67C2×#423—31no—
68C2×#417—31no—
69C2×#419—31no—
70#2297—31no—
71C2×#391—31no—
72#2056—31no—
73#2056—31no—
74#2056—31no—
75#2056—31no—
76#2055—31no—
77#2055—31no—
78#2055—31no—
79#2055D311yescharacteristic, complemented
80#1736—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×#67—21no—
84C23×Dic3—21no—
85C2×D3×Q8—22no—
86C2×D3×Q8—22no—
87C2×D3×Q8—22no—
88C2×D3×Q8—22no—
89C2×D3×Q8—22no—
90C2×D3×Q8D414yes—
91C2×#237—22no—
92C2×#237—22no—
93C2×#237—22no—
94C2×#237—22no—
95C2×#237—22no—
96C2×#237D414yes—
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3D411yescharacteristic
100C22×C4×D3D411yescharacteristic
101C22×C4×D3C2311yescharacteristic
102C22×Dic6—21no—
103C22×Dic6C2311yescharacteristic
104C22×Dic6C2311yescharacteristic
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C42C2311yescharacteristic
115C2×#217—21no—
116C2×#217—21no—
117C2×#216—22no—
118C2×#216—22no—
119C2×#216—22no—
120C2×#214—22no—
121C2×#214—22no—
122C2×#214—22no—
123C2×(C2×D3)⋊C4—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×Dic3⋊C4—21no—
127C2×C4×Dic3—21no—
128C2×C4×Dic3D411yescharacteristic
129C2×C4×Dic3D411yescharacteristic
130C2×C4×Dic3C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133#915—232no—
134C2×Dic12—22no—
135C2×Dic12—22no—
136C2×Dic12—22no—
137C2×ΓL(1,𝔽25)—22no—
138C2×ΓL(1,𝔽25)—22no—
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)—22no—
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)D414yes—
143#892—22no—
144#892—22no—
145D3×C4⋊C4—22no—
146D3×C4⋊C4—22no—
147C42×D3—22no—
148C42×D3—22no—
149C3×C4⋊C8—22no—
150C3×#103—22no—
151C3×#102—22no—
152C3×#95—21no—
153C3×#95—21no—
154#835—22no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166#816—22no—
167#816—22no—
168Dic3⋊C8—22no—
169Dic3⋊C8—22no—
170#810—22no—
171#810—22no—
172C4⋊(C3⋊C8)—22no—
173C22×#41—31no—
174C23×Q8—31no—
175C2×#137—64no—
176C2×#137—64no—
177C2×#137—64no—
178C22×Q16—31no—
179C22×Q16—31no—
180C22×SD16—31no—
181C22×SD16C2×D311yescharacteristic
182C22×M16—31no—
183C22×M16—31no—
184C2×#117—31no—
185C22×C4⋊C4—31no—
186C22×C42—31no—
187#423—64no—
188C2×C4⋊C8—31no—
189C2×C4⋊C8—31no—
190C2×C4⋊C8—31no—
191C2×C4⋊C8C2×D311yescharacteristic
192#419—64no—
193#417—64no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#103—31no—
199C2×#103C2×D311yescharacteristic
200C2×#102—31no—
201C2×#102C2×D311yescharacteristic
202#391—31no—
203#391—31no—
204#391—31no—
205#391—31no—
206#391—31no—
207#391—61no—
208#391—61no—
209#391C2×D311yescharacteristic
210#390—31no—
211#390C2×D311yescharacteristic
212#386—61no—
213#386—61no—
214C4×C22⋊C4—61no—
215C4×C22⋊C4—61no—
216C2×#95—61no—
217C2×#95—61no—
218#340—31no—
219#340—31no—
220#340—31no—
221#340C2×D311yescharacteristic
222C24×C3—21no—
223C23×D3C2×D411yescharacteristic
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8C2×D412yes—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4C2×D412yes—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C2×#67—24no—
243C2×#67—42no—
244C2×#67—42no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—24no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—42no—
251C22×Dic3—42no—
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255D3×Q8—28no—
256D3×Q8—28no—
257D3×Q8—44no—
258D3×Q8—44no—
259#237—28no—
260#237—28no—
261#237—44no—
262#237—44no—
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—24no—
266C2×C4×D3—22no—
267C2×C4×D3—22no—
268C2×C4×D3—41no—
269C2×C4×D3—41no—
270C2×C4×D3—42no—
271C2×C4×D3—42no—
272C2×C4×D3—42no—
273C2×C4×D3—42no—
274C2×C4×D3—42no—
275C2×C4×D3C2×D412yes—
276C2×C4×D3C2×D412yes—
277C2×C4×D3C2×D412yes—
278C2×C4×D3#4112yes—
279C2×C4×D3#4112yes—
280C2×C4×D3#4112yes—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—24no—
292C2×Dic6—42no—
293C2×Dic6—42no—
294C2×Dic6C2×D412yes—
295C2×Dic6C2×D412yes—
296C3×SD16—28no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8C2×D412yes—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—42no—
309C3×C42—21no—
310C3×C42—21no—
311#217—42no—
312#217—42no—
313#216—28no—
314#214—28no—
315(C2×D3)⋊C4—42no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320Dic3⋊C4—42no—
321C4×Dic3—21no—
322C4×Dic3—21no—
323C4×Dic3—22no—
324C4×Dic3—22no—
325C4×Dic3—42no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8C2×D412yes—
332Dic12—28no—
333ΓL(1,𝔽25)—28no—
334ΓL(1,𝔽25)—44no—
335C2×#41—34no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—62no—
339C2×#41—62no—
340C2×#41—62no—
341C22×Q8—34no—
342C22×Q8—31no—
343C22×Q8—31no—
344C22×Q8—61no—
345C22×Q8—62no—
346C22×Q8—62no—
347C22×Q8—62no—
348C22×Q8—62no—
349C22×Q8—62no—
350C22×Q8C22×D311yescharacteristic
351C22×D4—61no—
352C22×D4C22×D311yescharacteristic
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—61no—
357C23×C4—61no—
358C23×C4—61no—
359#137—632no—
360C2×Q16—62no—
361C2×Q16—62no—
362C2×Q16—62no—
363C2×Q16—62no—
364C2×Q16—62no—
365C2×Q16—62no—
366C2×SD16—22no—
367C2×SD16—22no—
368C2×SD16—22no—
369C2×SD16—62no—
370C2×SD16—62no—
371C2×SD16—62no—
372C2×M16—34no—
373C2×M16—62no—
374C2×M16—62no—
375C2×M16—62no—
376C2×M16—62no—
377C2×M16—62no—
378C22×C8—31no—
379C22×C8—31no—
380C22×C8C22×D311yescharacteristic
381C22×C8C22×D311yescharacteristic
382#117—62no—
383#117—62no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C42—31no—
397C2×C42—31no—
398C2×C42—31no—
399C2×C42—62no—
400C2×C42—62no—
401C2×C42—61no—
402C2×C42C22×D311yescharacteristic
403C4⋊C8—22no—
404C4⋊C8—62no—
405C4⋊C8—62no—
406C4⋊C8—62no—
407#103—22no—
408#103—62no—
409#103—62no—
410#103—62no—
411#103—62no—
412#103—62no—
413#102—22no—
414#102—62no—
415#95—21no—
416#95—21no—
417#95—61no—
418#95—61no—
419#95—61no—
420#95—61no—
421#95—61no—
422#95—61no—
423#95—61no—
424#95—61no—
425#95—61no—
426#95—61no—
427C23×C3—22no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3C22×D411yescharacteristic
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3#12112yes—
440C22×D3#12112yes—
441C22×D3#12112yes—
442C3×Q8—22no—
443C3×Q8—22no—
444C3×Q8—41no—
445C3×Q8—41no—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—41no—
449C3×D4—41no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4#13712yescomplemented
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471#67—48no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—48no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3#12112yes—
491C2×Dic3#12112yes—
492C2×Dic3#12112yes—
493C2×Dic3#13712yescomplemented
494C4×D3—44no—
495C4×D3—44no—
496C4×D3—48no—
497C4×D3—84no—
498C4×D3#12014yes—
499C4×D3#12314yes—
500C4×D3#12314yes—
501C4×D3#12414yes—
502Dic6—22no—
503Dic6—22no—
504Dic6—22no—
505Dic6—22no—
506Dic6—41no—
507Dic6—41no—
508Dic6—41no—
509Dic6—41no—
510Dic6—48no—
511C3×C8—22no—
512C3×C8—41no—
513C3⋊C8—22no—
514C3⋊C8—41no—
515C24—21no—
516C24—31no—
517#41—68no—
518#41—68no—
519#41—124no—
520#41—124no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—32no—
527C2×Q8—32no—
528C2×Q8—64no—
529C2×Q8—68no—
530C2×Q8—68no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—122no—
542C2×Q8—122no—
543C2×Q8—124no—
544C2×Q8—124no—
545C2×Q8D3×D412yes—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—64no—
552C2×D4—122no—
553C2×D4—122no—
554C2×D4D3×D412yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—31no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—32no—
563C22×C4—32no—
564C22×C4—32no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—64no—
571C22×C4—64no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—62no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—121no—
578C22×C4—121no—
579C22×C4—122no—
580C22×C4—122no—
581C22×C4—122no—
582C22×C4—122no—
583C22×C4—122no—
584C22×C4—122no—
585C22×C4—122no—
586C22×C4D3×D411yescharacteristic
587C22×C4D3×D411yescharacteristic
588C22×C4C23×D311yescharacteristic
589Q16—68no—
590Q16—68no—
591SD16—28no—
592SD16—68no—
593M16—68no—
594M16—124no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—32no—
601C2×C8—61no—
602C2×C8—61no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8D3×D412yes—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—122no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—122no—
619C22⋊C4—122no—
620C22⋊C4—122no—
621C42—21no—
622C42—21no—
623C42—62no—
624C42—62no—
625C42—61no—
626C42—61no—
627C42—122no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3C2×#12111yescharacteristic
636C22×C3C2×#12111yescharacteristic
637C22×C3C2×#12111yescharacteristic
638C22×C3C2×#13711yescharacteristic
639C22×C3C2×#13711yescharacteristic
640C22×C3#57511yescharacteristic
641C22×C3#57511yescharacteristic
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—22no—
648C2×D3#39414yes—
649C3×C4—22no—
650C3×C4—42no—
651C3×C4—41no—
652C3×C4—81no—
653C3×C4—81no—
654C3×C4C2×#12011yescharacteristic
655C3×C4C2×#12311yescharacteristic
656C3×C4C2×#12311yescharacteristic
657C3×C4C2×#12411yescharacteristic
658Dic3—22no—
659Dic3—42no—
660Dic3—42no—
661Dic3—41no—
662Dic3—81no—
663Dic3—81no—
664Dic3#39414yes—
665C23—22no—
666C23—32no—
667C23—32no—
668C23—32no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23C2×D3×D411yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—41no—
683Q8—41no—
684Q8—62no—
685Q8—62no—
686Q8—62no—
687Q8—62no—
688Q8—128no—
689Q8—121no—
690Q8—121no—
691Q8—121no—
692Q8—121no—
693D4—22no—
694D4—22no—
695D4—41no—
696D4—41no—
697D4—128no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—34no—
708C2×C4—34no—
709C2×C4—34no—
710C2×C4—34no—
711C2×C4—32no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—124no—
728C2×C4—128no—
729C2×C4—124no—
730C2×C4—128no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—244no—
742C2×C4#91512yescomplemented
743C2×C4C2×D3×D411yescharacteristic
744C2×C4C2×D3×D411yescharacteristic
745C2×C4C2×D3×D411yescharacteristic
746C2×C4D3×#4111yescharacteristic
747C2×C4D3×#4111yescharacteristic
748C2×C4D3×#4111yescharacteristic
749C8—22no—
750C8—41no—
751C8—62no—
752C8—121no—
753C2×C3—82no—
754C2×C3C2×#39411yescharacteristic
755C2×C3#303711yescharacteristic
756C2×C3#303711yescharacteristic
757C2×C3#303911yescharacteristic
758C2×C3#304011yescharacteristic
759C2×C3#305611yescharacteristic
760C2×C3#305611yescharacteristic
761D3—24no—
762C22—34no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—62no—
767C22—62no—
768C22—62no—
769C22—62no—
770C22—62no—
771C22—62no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22D3×#12111yescharacteristic
777C22D3×#12111yescharacteristic
778C22D3×#12111yescharacteristic
779C22C2×#91511yescharacteristic
780C22#576811yescharacteristic
781C22#577311yescharacteristic
782C22D3×#13711yescharacteristic
783C4—22no—
784C4—34no—
785C4—42no—
786C4—41no—
787C4—62no—
788C4—81no—
789C4—81no—
790C4—121no—
791C4—122no—
792C4—122no—
793C4—241no—
794C4—241no—
795C4D3×#12011yescharacteristic
796C4D3×#12311yescharacteristic
797C4D3×#12311yescharacteristic
798C4D3×#12411yescharacteristic
799C3#2354711yescharacteristic, complemented, Sylow
800C2—64no—
801C2—82no—
802C2D3×#39411yescharacteristic
803C2#8038311yescharacteristic
804C2#8042911yescharacteristic
805C2#8053511yescharacteristic
806C2#8059811yescharacteristic
807C2#8065811yescharacteristic
808C2#8080611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2055C2
socleC23×C3C22×D4
prime radicalC22×#237C22
hypercenter#2055D3
hypocenterC3#23547
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. C2×#4837C2semidirect
3. C2×#4802C2semidirect
5. D3×#391C2semidirect
7. C3×#2055C2semidirect
8. #72051C2semidirect
9. #70487C2semidirect
10. #70285C2semidirect
11. #70217C2semidirect
12. #69681C2semidirect
13. #69651C2semidirect
14. #68867C2semidirect
15. #68864C2semidirect
79. #2055D3semidirect
464. C2×C3×C4#137semidirect
493. C2×Dic3#137semidirect
742. C2×C4#915semidirect
799. C3#23547semidirect

Maximal subgroups

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

subgroupindex
C22×#9152
C2×#48372
C2×#48022
C2×#47712
D3×#3912
#762902
C3×#20552
#720512
#704872
#702852
#702172
#696812
#696512
#688672
#688642
#235473