Finite Group Databasebeta

← #10944127

Subgroups — #10944127

Order 768.

1588 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5545C211yesmaximal, characteristic, complemented
2C2×#5016C211yesmaximal, characteristic, complemented
3C2×#4844C211yesmaximal, characteristic, complemented
4C2×#4776C211yesmaximal, characteristic, complemented
5C2×#4773C211yesmaximal, characteristic
6#74370C211yesmaximal, characteristic, complemented
7C3×#1802C211yesmaximal, characteristic, complemented
8#70476C211yesmaximal, characteristic, complemented
9#70172C211yesmaximal, characteristic, complemented
10#70171C211yesmaximal, characteristic, complemented
11#69584C211yesmaximal, characteristic, complemented
12#68897C211yesmaximal, characteristic, complemented
13#68896C211yesmaximal, characteristic, complemented
14#68881C211yesmaximal, characteristic, complemented
15#68879C211yesmaximal, characteristic, complemented
16#32917—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×D4×Dic3C2211yescharacteristic
20C22×#214C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×C4×#67—21no—
23C22×(C2×D3)⋊C4—21no—
24C22×D24C2211yescharacteristic
25C22×#204C2211yescharacteristic
26#5545—24no—
27#5545—24no—
28C2×#897C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#893C2211yescharacteristic
31C2×#892C2211yescharacteristic
32C2×#67⋊C4—21no—
33C2×D3×C22⋊C4—21no—
34C2×#875C2211yescharacteristic, complemented
35C2×C4×D12C2211yescharacteristic
36C2×#872C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C3×#384C2211yescharacteristic, complemented
41C2×#821C2211yescharacteristic, complemented
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#816C2211yescharacteristic, complemented
45#5016—24no—
46#4994—21no—
47#4994—21no—
48#4991—21no—
49#4991—21no—
50#4988C2211yescharacteristic, complemented
51#4973C2211yescharacteristic, complemented
52C2×#810C2211yescharacteristic, complemented
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic, complemented
56C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57#4844—24no—
58#4776—24no—
59#4773—24no—
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62#4550C2211yescharacteristic, complemented
63#4550C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#518—31no—
67C2×#463—31no—
68C2×#463—31no—
69C2×#450—31no—
70C2×#447—31no—
71#2620—31no—
72#1879—31no—
73#1879—31no—
74#1877—31no—
75#1877—31no—
76#1875—31no—
77#1873—31no—
78#1802—31no—
79#1802D311yescharacteristic, complemented
80#1798—31no—
81C24×D3—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C22×#67—21no—
85C23×Dic3—21no—
86C2×D3×D4—22no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4D414yes—
92C22×D12—21no—
93C22×D12C2311yescharacteristic
94C22×D12C2311yescharacteristic
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×C4×D3C2311yescharacteristic
98C22×Dic6C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×C4×D4—22no—
102C3×C4×D4D414yescomplemented
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111D4×Dic3—22no—
112D4×Dic3—22no—
113C2×#214—22no—
114C2×#214—22no—
115C2×#214—22no—
116C2×#213—22no—
117C2×#213—22no—
118C2×#213—22no—
119C4×#67—28no—
120C2×(C2×D3)⋊C4—28no—
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)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4D411yescharacteristic
135C2×Dic3⋊C4D411yescharacteristic
136C2×C4×Dic3—21no—
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C2×D24—22no—
141C2×D24—22no—
142C2×D24—22no—
143C2×#204—22no—
144C2×#204—22no—
145C2×#204—22no—
146#897—22no—
147#897—22no—
148#895—22no—
149#895—22no—
150#893—22no—
151#893—22no—
152#892—22no—
153#892—22no—
154#67⋊C4—28no—
155D3×C22⋊C4—28no—
156#875—22no—
157#875—22no—
158C4×D12—22no—
159C4×D12D414yescomplemented
160#872—22no—
161#872—22no—
162C3×C4⋊C8—22no—
163C3×#102—22no—
164C3×#102—22no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167#821—22no—
168(C2×D3)⋊C8—22no—
169(C2×D3)⋊C8—22no—
170#816—22no—
171#810—22no—
172#809—22no—
173#809—22no—
174#809—22no—
175C4⋊(C3⋊C8)—22no—
176C23×D4—31no—
177C22×SD16—31no—
178C22×SD16—31no—
179C22×D8—31no—
180C22×D8—31no—
181C2×#124—31no—
182C2×C22⋊Q8—31no—
183C2×#121—31no—
184#518—64no—
185#518—64no—
186C2×C4×D4—31no—
187C2×C4×D4—31no—
188C2×C4×D4—31no—
189C2×C4×D4—61no—
190C2×C4×D4—61no—
191C2×C4×D4C2×D311yescharacteristic
192C2×#117—31no—
193C2×#117—31no—
194C22×C22⋊C4—61no—
195C22×C22⋊C4—61no—
196#463—64no—
197#463—64no—
198#450—64no—
199#447—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8C2×D311yescharacteristic, complemented
202C2×#103—31no—
203C2×#103—31no—
204C2×#102—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102C2×D311yescharacteristic
209C2×#102C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212#396—61no—
213#396—61no—
214#394—61no—
215#394—61no—
216#391—31no—
217#390—31no—
218#384C2×D311yescharacteristic, complemented
219#340—31no—
220#340—31no—
221#340C2×D311yescharacteristic, complemented
222#340C2×D311yescharacteristic, complemented
223#336—31no—
224#336—31no—
225C24×C3—21no—
226C23×D3—21no—
227C23×D3—24no—
228C23×D3—24no—
229C23×D3—24no—
230C23×D3—21no—
231C23×D3—81no—
232C23×D3—81no—
233C23×D3—81no—
234C23×D3—81no—
235C23×D3C2×D411yescharacteristic
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4C2×D412yes—
240C2×C3×D4C2×D412yes—
241C2×C3×D4#4112yes—
242C22×C3×C4—21no—
243C22×C3×C4—24no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—81no—
247C22×C3×C4—81no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2411yescharacteristic
251C2×#67—24no—
252C2×#67—24no—
253C2×#67—24no—
254C22×Dic3—21no—
255C22×Dic3—24no—
256C22×Dic3—21no—
257C22×Dic3—81no—
258C22×Dic3—81no—
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262D3×D4—28no—
263D3×D4—28no—
264D3×D4—28no—
265D3×D4—28no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—42no—
276C2×D12—81no—
277C2×D12—81no—
278C2×D12C2×D412yes—
279C2×D12C2×D412yes—
280C2×D12#4112yes—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—24no—
286C2×C4×D3—24no—
287C2×C4×D3—81no—
288C2×C4×D3—81no—
289C2×C4×D3—81no—
290C2×C4×D3—81no—
291C2×C4×D3C2×D412yes—
292C2×C4×D3#4112yes—
293C2×Dic6—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6—21no—
298C2×Dic6—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—81no—
311C3×C4⋊C4—81no—
312C3×C4⋊C4C2×D412yes—
313C3×C22⋊C4—24no—
314C3×C42C2×D412yes—
315C3×C42C2×D412yes—
316#217—24no—
317#214—44no—
318#213—44no—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—24no—
321(C2×D3)⋊C4—22no—
322(C2×D3)⋊C4—22no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326(C2×D3)⋊C4—42no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4—81no—
329(C2×D3)⋊C4—81no—
330C4⋊Dic3—21no—
331C4⋊Dic3—42no—
332C4⋊Dic3C2×D412yes—
333Dic3⋊C4—22no—
334Dic3⋊C4—22no—
335C4×Dic3—24no—
336C4×Dic3—21no—
337C4×Dic3—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344D24—44no—
345#204—44no—
346C25—61no—
347C22×Q8—31no—
348C22×D4—34no—
349C22×D4—31no—
350C22×D4—31no—
351C22×D4—61no—
352C22×D4—62no—
353C22×D4—61no—
354C22×D4—62no—
355C22×D4—62no—
356C22×D4—62no—
357C22×D4—62no—
358C22×D4C22×D311yescharacteristic
359C23×C4—21no—
360C23×C4—31no—
361C23×C4—61no—
362C23×C4—61no—
363C23×C4—61no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×SD16—62no—
367C2×SD16—62no—
368C2×SD16—62no—
369C2×SD16—62no—
370C2×D8—62no—
371C2×D8—62no—
372C2×D8—62no—
373C2×D8—62no—
374C2×D8—62no—
375C2×D8—62no—
376C22×C8—31no—
377C22×C8—31no—
378C22×C8C22×D311yescharacteristic
379C22×C8C22×D311yescharacteristic
380#124—62no—
381#124—62no—
382C22⋊Q8—62no—
383C22⋊Q8—62no—
384#121—62no—
385#121—62no—
386C4×D4—22no—
387C4×D4—34no—
388C4×D4—68no—
389C4×D4—62no—
390C4×D4—62no—
391C4×D4—68no—
392C4×D4—62no—
393C4×D4—62no—
394C4×D4—62no—
395C4×D4D1214yescomplemented
396#117—62no—
397#117—62no—
398#117—62no—
399#117—62no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—31no—
411C2×C22⋊C4—31no—
412C2×C22⋊C4—68no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—68no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C42—31no—
425C2×C42—61no—
426C2×C42C22×D311yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—62no—
429#103—62no—
430#103—62no—
431#102—22no—
432#102—22no—
433#102—62no—
434#102—62no—
435#102—62no—
436#102—62no—
437C22⋊C8—62no—
438C22⋊C8—62no—
439#95—61no—
440#95—61no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3C22×D411yescharacteristic
449C22×D3—21no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—21no—
453C22×D3—22no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—216no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—84no—
471C22×D3—84no—
472C22×D3—84no—
473C22×D3—84no—
474C22×D3—84no—
475C22×D3—84no—
476C22×D3#12112yes—
477C3×D4—22no—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4#12114yes—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—84no—
495C2×C3×C4#12012yes—
496C2×C3×C4#12012yes—
497C2×C3×C4C22×D411yescharacteristic
498C2×C3×C4C22×D411yescharacteristic
499C2×C3×C4C22×D411yescharacteristic
500C2×C3×C4C2×#4111yescharacteristic
501C2×C3×C4C2×#4111yescharacteristic
502C2×C3×C4C2×#4111yescharacteristic
503#67—216no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—84no—
519C2×Dic3#12112yes—
520D12—22no—
521D12—22no—
522D12—22no—
523D12—41no—
524D12—41no—
525D12—41no—
526D12—41no—
527D12—84no—
528D12#12114yes—
529C4×D3—22no—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—84no—
534C4×D3—84no—
535Dic6—41no—
536Dic6—41no—
537Dic6—41no—
538Dic6—41no—
539C3×C8—41no—
540C3×C8—41no—
541C3⋊C8—41no—
542C3⋊C8—41no—
543C24—21no—
544C24—31no—
545C24—64no—
546C24—64no—
547C24—64no—
548C24—61no—
549C24—61no—
550C24—241no—
551C24—241no—
552C24—241no—
553C24—241no—
554C2×Q8—61no—
555C2×Q8—61no—
556C2×Q8—61no—
557C2×Q8—61no—
558C2×Q8—61no—
559C2×Q8—61no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—32no—
564C2×D4—32no—
565C2×D4—32no—
566C2×D4—64no—
567C2×D4—68no—
568C2×D4—68no—
569C2×D4—68no—
570C2×D4—64no—
571C2×D4—64no—
572C2×D4—68no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—122no—
583C2×D4—241no—
584C2×D4—241no—
585C2×D4C2×D1212yes—
586C2×D4D3×D412yes—
587C2×D4#23912yes—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—31no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—64no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—64no—
604C22×C4—64no—
605C22×C4—61no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—241no—
609C22×C4—241no—
610C22×C4—241no—
611C22×C4—241no—
612C22×C4—241no—
613C22×C4—241no—
614C22×C4D3×D411yescharacteristic
615C22×C4D3×D411yescharacteristic
616C22×C4C23×D311yescharacteristic
617SD16—124no—
618SD16—124no—
619D8—124no—
620D8—124no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—61no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C2×C8—61no—
632C2×C8—61no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—32no—
639C4⋊C4—62no—
640C4⋊C4—62no—
641C4⋊C4—61no—
642C4⋊C4—81no—
643C4⋊C4—81no—
644C4⋊C4—122no—
645C4⋊C4C2×D1212yes—
646C22⋊C4—24no—
647C22⋊C4—64no—
648C22⋊C4—64no—
649C22⋊C4—64no—
650C22⋊C4—62no—
651C22⋊C4—62no—
652C22⋊C4—64no—
653C22⋊C4—122no—
654C22⋊C4—122no—
655C22⋊C4—122no—
656C22⋊C4—122no—
657C22⋊C4—241no—
658C22⋊C4—241no—
659C42—64no—
660C42—61no—
661C42—61no—
662C42C2×D1212yes—
663C42D3×D412yes—
664C22×C3—24no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3C2×#12011yescharacteristic
672C22×C3C2×#12111yescharacteristic
673C22×C3#52511yescharacteristic
674C22×C3#57611yescharacteristic
675C22×C3#57611yescharacteristic
676C22×C3#57711yescharacteristic
677C22×C3#57711yescharacteristic
678C2×D3—22no—
679C2×D3—24no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—42no—
685C2×D3—42no—
686C2×D3—42no—
687C2×D3—42no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—816no—
693C2×D3—81no—
694C2×D3—81no—
695C2×D3—81no—
696C2×D3—81no—
697C2×D3—81no—
698C2×D3—81no—
699C2×D3—81no—
700C3×C4—22no—
701C3×C4—22no—
702C3×C4—42no—
703C3×C4—81no—
704C3×C4—81no—
705C3×C4C2×#12111yescharacteristic
706C3×C4C2×#12111yescharacteristic
707C3×C4#52511yescharacteristic
708C3×C4#52511yescharacteristic
709Dic3—22no—
710Dic3—41no—
711Dic3—42no—
712Dic3—41no—
713Dic3—81no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—32no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—616no—
723C23—61no—
724C23—62no—
725C23—61no—
726C23—61no—
727C23—61no—
728C23—61no—
729C23—62no—
730C23—61no—
731C23—62no—
732C23—121no—
733C23—121no—
734C23—121no—
735C23—121no—
736C23—121no—
737C23—121no—
738C23—121no—
739C23—121no—
740C23—121no—
741C23—121no—
742C23—121no—
743C23—244no—
744C23—244no—
745C23—244no—
746C23—244no—
747C23—244no—
748C23—244no—
749C23C2×D3×D411yescharacteristic
750Q8—121no—
751Q8—121no—
752Q8—121no—
753Q8—121no—
754D4—22no—
755D4—22no—
756D4—22no—
757D4—34no—
758D4—616no—
759D4—62no—
760D4—62no—
761D4—62no—
762D4—121no—
763D4—121no—
764D4—121no—
765D4—121no—
766D4—244no—
767D4#89514yes—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—32no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—84no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—244no—
802C2×C4—244no—
803C2×C4—244no—
804C2×C4#88212yes—
805C2×C4#88212yes—
806C2×C4C22×D1211yescharacteristic
807C2×C4C2×D3×D411yescharacteristic
808C2×C4C2×D3×D411yescharacteristic
809C2×C4C2×#23911yescharacteristic
810C2×C4D3×#4111yescharacteristic
811C2×C4D3×#4111yescharacteristic
812C8—41no—
813C8—41no—
814C8—121no—
815C8—121no—
816C2×C3—44no—
817C2×C3#284711yescharacteristic
818C2×C3#301211yescharacteristic
819C2×C3#301211yescharacteristic
820C2×C3#304111yescharacteristic
821C2×C3#304211yescharacteristic
822C2×C3#311811yescharacteristic
823C2×C3#311811yescharacteristic
824D3—42no—
825D3—44no—
826D3—161no—
827C22—24no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—62no—
835C22—62no—
836C22—64no—
837C22—62no—
838C22—122no—
839C22—121no—
840C22—122no—
841C22—121no—
842C22—122no—
843C22—121no—
844C22—122no—
845C22—122no—
846C22—121no—
847C22—122no—
848C22—2416no—
849C22—241no—
850C22—241no—
851C22—241no—
852C22—241no—
853C22—241no—
854C22—241no—
855C22—241no—
856C22C2×#88211yescharacteristic
857C22D3×#12111yescharacteristic
858C22#562711yescharacteristic
859C22#575711yescharacteristic
860C22#576211yescharacteristic
861C22#577411yescharacteristic
862C22#577811yescharacteristic
863C4—22no—
864C4—22no—
865C4—42no—
866C4—62no—
867C4—81no—
868C4—81no—
869C4—121no—
870C4—122no—
871C4—121no—
872C4—241no—
873C4C2×#89511yescharacteristic
874C4#552411yescharacteristic
875C4D3×#12111yescharacteristic
876C4#562711yescharacteristic
877C3#3291711yescharacteristic, complemented, Sylow
878C2—44no—
879C2—122no—
880C2—124no—
881C2—481no—
882C2#7404811yescharacteristic
883C2#7874711yescharacteristic
884C2#7888611yescharacteristic
885C2#8033411yescharacteristic
886C2#8043011yescharacteristic
887C2#8095211yescharacteristic
888C2#8104811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1802C2
socleC23×C3C22×D4
prime radicalC2×#4773C2
hypercenter#1802D3
hypocenterC3#32917
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. C2×#5545C2semidirect
2. C2×#5016C2semidirect
3. C2×#4844C2semidirect
4. C2×#4776C2semidirect
6. #74370C2semidirect
7. C3×#1802C2semidirect
8. #70476C2semidirect
9. #70172C2semidirect
10. #70171C2semidirect
11. #69584C2semidirect
12. #68897C2semidirect
13. #68896C2semidirect
14. #68881C2semidirect
15. #68879C2semidirect
34. C2×#875C22semidirect
37. C2×C3×C4⋊C8C22semidirect
40. C3×#384C22semidirect
41. C2×#821C22semidirect
44. C2×#816C22semidirect
50. #4988C22semidirect
51. #4973C22semidirect
52. C2×#810C22semidirect
55. C2×#809C22semidirect
56. C2×C4⋊(C3⋊C8)C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. #4550C22semidirect
63. #4550C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
79. #1802D3semidirect
102. C3×C4×D4D4semidirect
159. C4×D12D4semidirect
201. C2×C4⋊C8C2×D3semidirect
218. #384C2×D3semidirect
221. #340C2×D3semidirect
222. #340C2×D3semidirect
395. C4×D4D12semidirect
877. C3#32917semidirect

Maximal subgroups

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

subgroupindex
C2×#55452
C2×#50162
C2×#48442
C2×#47762
C2×#47732
#743702
C3×#18022
#704762
#701722
#701712
#695842
#688972
#688962
#688812
#688792
#329173