Finite Group Databasebeta

← #10944121

Subgroups — #10944121

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×C3×#463C211yesmaximal, characteristic, complemented
3C2×#5169C211yesmaximal, characteristic, complemented
4C2×#5156C211yesmaximal, characteristic
5#83001C211yesmaximal, characteristic, complemented
6C2×#5057C211yesmaximal, characteristic, complemented
7#72047C211yesmaximal, characteristic, complemented
8#72037C211yesmaximal, characteristic, complemented
9#71604C211yesmaximal, characteristic, complemented
10#70479C211yesmaximal, characteristic, complemented
11#70476C211yesmaximal, characteristic, complemented
12#70276C211yesmaximal, characteristic, complemented
13#70269C211yesmaximal, characteristic, complemented
14#70208C211yesmaximal, characteristic, complemented
15#70201C211yesmaximal, characteristic, complemented
16#32917—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×#124C2211yescharacteristic, complemented
21C2×C3×C4×D4C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26C22×#213C2211yescharacteristic
27C2×C4×#67—21no—
28C22×(C2×D3)⋊C4—21no—
29#5545—24no—
30#5545—24no—
31C2×#893C2211yescharacteristic
32C2×#892C2211yescharacteristic
33C2×#67⋊C4—21no—
34C2×D3×C22⋊C4—21no—
35C2×C4×D12C2211yescharacteristic
36C2×#872C2211yescharacteristic
37C3×#463—24no—
38C2×C3×C4⋊C8C2211yescharacteristic, complemented
39C2×C3×#103C2211yescharacteristic, complemented
40C2×C3×#102C2211yescharacteristic, complemented
41#5229C2211yescharacteristic, complemented
42C2×#835C2211yescharacteristic, complemented
43#5221C2211yescharacteristic, complemented
44C2×#832C2211yescharacteristic
45C2×#832C2211yescharacteristic
46C2×#832C2211yescharacteristic, complemented
47#5169—24no—
48#5156—24no—
49C2×#821C2211yescharacteristic
50C2×#821C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53#5057—24no—
54#4961—21no—
55#4961—21no—
56#4948—21no—
57#4948—21no—
58#4935C2211yescharacteristic, complemented
59C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
60#4551C2211yescharacteristic, complemented
61#4551C2211yescharacteristic, complemented
62#4550C2211yescharacteristic, complemented
63#4550C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#518—31no—
67C2×#463—31no—
68C2×#463D311yescharacteristic, complemented
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#1802—31no—
80#1798—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C22×#67—21no—
87C22×#67—21no—
88C23×Dic3—21no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4—22no—
94C2×D3×D4D414yes—
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C22×C4×D3—21no—
98C22×C4×D3C2311yescharacteristic
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×D8—22no—
103C2×C3×D8—22no—
104C2×C3×D8—22no—
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×#124—22no—
108C3×#124—22no—
109C3×C4×D4—22no—
110C3×C4×D4D414yescomplemented
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C42C2311yescharacteristic
116C2×#217—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#217—21no—
120#946—22no—
121#946—22no—
122C2×#215—22no—
123C2×#215—22no—
124C2×#215—22no—
125#938—22no—
126#938—22no—
127D4×Dic3—22no—
128D4×Dic3—22no—
129C2×#213—22no—
130C2×#213—22no—
131C2×#213—22no—
132C4×#67—28no—
133C2×(C2×D3)⋊C4—28no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4D411yescharacteristic
139C2×(C2×D3)⋊C4D411yescharacteristic
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3—21no—
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4D411yescharacteristic
147C2×Dic3⋊C4D411yescharacteristic
148C2×C4×Dic3—21no—
149C2×C4×Dic3C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152#893—22no—
153#893—22no—
154#892—22no—
155#892—22no—
156#67⋊C4—28no—
157D3×C22⋊C4—28no—
158C4×D12—22no—
159C4×D12D414yescomplemented
160#872—22no—
161#872—22no—
162C3×C4⋊C8—22no—
163C3×#103—22no—
164C3×#102—22no—
165#835—22no—
166#832—22no—
167#832—22no—
168#832—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#821—22no—
172#821—22no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—22no—
175C4⋊(C3⋊C8)—22no—
176C23×D4—31no—
177C22×SD16—31no—
178C22×SD16C2×D311yescharacteristic
179C22×D8—31no—
180C22×D8C2×D311yescharacteristic
181C2×#124C2×D311yescharacteristic, complemented
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—24no—
197#463—64no—
198#450—64no—
199#447—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8C2×D311yescharacteristic, complemented
202C2×#103—31no—
203C2×#103C2×D311yescharacteristic, complemented
204C2×#102—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102C2×D311yescharacteristic, complemented
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#384—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223#336—31no—
224#336—31no—
225C24×C3—21no—
226C24×C3—21no—
227C23×D3—21no—
228C23×D3—24no—
229C23×D3—24no—
230C23×D3—24no—
231C23×D3—81no—
232C23×D3—81no—
233C23×D3—81no—
234C23×D3—81no—
235C23×D3C2×D411yescharacteristic
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4C2×D412yes—
252C2×C3×D4C2×D412yes—
253C2×C3×D4#4112yes—
254C22×C3×C4—21no—
255C22×C3×C4—24no—
256C22×C3×C4—21no—
257C22×C3×C4—81no—
258C22×C3×C4—81no—
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2411yescharacteristic
262C2×#67—24no—
263C2×#67—24no—
264C2×#67—24no—
265C2×#67—42no—
266C2×#67—81no—
267C2×#67—81no—
268C22×Dic3—21no—
269C22×Dic3—24no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—81no—
273C22×Dic3—81no—
274C22×Dic3C2×D411yescharacteristic
275C22×Dic3C2×D411yescharacteristic
276C22×Dic3C2×D411yescharacteristic
277D3×D4—28no—
278D3×D4—28no—
279D3×D4—28no—
280D3×D4—28no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12C2×D412yes—
285C2×D12C2×D412yes—
286C2×D12#4112yes—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—24no—
292C2×C4×D3—24no—
293C2×C4×D3—81no—
294C2×C4×D3—81no—
295C2×C4×D3—81no—
296C2×C4×D3—81no—
297C2×C4×D3C2×D412yes—
298C2×C4×D3#4112yes—
299C3×SD16—44no—
300C3×D8—44no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4C2×D412yes—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—42no—
312C3×C42C2×D412yes—
313C3×C42C2×D412yes—
314#217—24no—
315#217—42no—
316#217—81no—
317#217—81no—
318#215—44no—
319#213—44no—
320(C2×D3)⋊C4—24no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—22no—
323(C2×D3)⋊C4—22no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—42no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—81no—
332C4⋊Dic3—81no—
333C4⋊Dic3C2×D412yes—
334Dic3⋊C4—22no—
335Dic3⋊C4—22no—
336Dic3⋊C4—42no—
337C4×Dic3—24no—
338C4×Dic3—21no—
339C4×Dic3—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C25—61no—
347C22×Q8C22×D311yescharacteristic
348C22×D4—34no—
349C22×D4—31no—
350C22×D4—62no—
351C22×D4—61no—
352C22×D4—62no—
353C22×D4—62no—
354C22×D4—62no—
355C22×D4—62no—
356C22×D4—61no—
357C22×D4C22×D311yescharacteristic
358C22×D4C22×D311yescharacteristic
359C23×C4—21no—
360C23×C4—31no—
361C23×C4—61no—
362C23×C4—61no—
363C23×C4—61no—
364C2×SD16—22no—
365C2×SD16—22no—
366C2×SD16—22no—
367C2×SD16—62no—
368C2×SD16—62no—
369C2×SD16—62no—
370C2×D8—22no—
371C2×D8—22no—
372C2×D8—22no—
373C2×D8—62no—
374C2×D8—62no—
375C2×D8—62no—
376C22×C8—31no—
377C22×C8—31no—
378C22×C8C22×D311yescharacteristic
379C22×C8C22×D311yescharacteristic
380#124—22no—
381#124—22no—
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×D4#6714yescomplemented
396#117—62no—
397#117—62no—
398#117—62no—
399#117—62no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—61no—
406C2×C4⋊C4—61no—
407C2×C4⋊C4—61no—
408C2×C4⋊C4C22×D311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—31no—
413C2×C22⋊C4—31no—
414C2×C22⋊C4—68no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—68no—
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—22no—
430#103—62no—
431#102—22no—
432#102—62no—
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×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3C22×D411yescharacteristic
456C22×D3—21no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—21no—
460C22×D3—22no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—216no—
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×Q8—41no—
478C3×Q8—41no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×D4—22no—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4#12114yes—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—84no—
500C2×C3×C4#12012yes—
501C2×C3×C4#12012yes—
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C22×D411yescharacteristic
504C2×C3×C4C22×D411yescharacteristic
505C2×C3×C4C2×#4111yescharacteristic
506C2×C3×C4C2×#4111yescharacteristic
507C2×C3×C4C2×#4111yescharacteristic
508#67—216no—
509#67—84no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—22no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—84no—
528C2×Dic3#12112yes—
529D12—22no—
530D12—22no—
531D12—22no—
532D12#12114yes—
533C4×D3—22no—
534C4×D3—22no—
535C4×D3—22no—
536C4×D3—22no—
537C4×D3—84no—
538C4×D3—84no—
539C3×C8—41no—
540C3×C8—41no—
541C3⋊C8—41no—
542C3⋊C8—41no—
543C24—21no—
544C24—21no—
545C24—31no—
546C24—64no—
547C24—64no—
548C24—64no—
549C24—61no—
550C24—241no—
551C24—241no—
552C24—241no—
553C24—241no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—32no—
570C2×D4—32no—
571C2×D4—32no—
572C2×D4—64no—
573C2×D4—68no—
574C2×D4—68no—
575C2×D4—68no—
576C2×D4—64no—
577C2×D4—64no—
578C2×D4—68no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—122no—
583C2×D4—241no—
584C2×D4—241no—
585C2×D4D3×D412yes—
586C2×D4#23712yes—
587C2×D4C2×#6712yes—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—31no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—64no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—64no—
603C22×C4—64no—
604C22×C4—61no—
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—44no—
618SD16—124no—
619D8—44no—
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—32no—
635C4⋊C4—62no—
636C4⋊C4—62no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—122no—
643C4⋊C4—241no—
644C4⋊C4—241no—
645C4⋊C4C2×#6712yes—
646C22⋊C4—24no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—64no—
650C22⋊C4—64no—
651C22⋊C4—64no—
652C22⋊C4—62no—
653C22⋊C4—62no—
654C22⋊C4—64no—
655C22⋊C4—122no—
656C22⋊C4—122no—
657C22⋊C4—241no—
658C22⋊C4—241no—
659C42—64no—
660C42—61no—
661C42—61no—
662C42D3×D412yes—
663C42C2×#6712yes—
664C22×C3—24no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3C2×#12011yescharacteristic
679C22×C3C2×#12111yescharacteristic
680C22×C3#52511yescharacteristic
681C22×C3#57611yescharacteristic
682C22×C3#57611yescharacteristic
683C22×C3#57711yescharacteristic
684C22×C3#57711yescharacteristic
685C2×D3—22no—
686C2×D3—24no—
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—42no—
692C2×D3—42no—
693C2×D3—42no—
694C2×D3—42no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—816no—
700C3×C4—22no—
701C3×C4—22no—
702C3×C4—42no—
703C3×C4—81no—
704C3×C4C2×#12111yescharacteristic
705C3×C4C2×#12111yescharacteristic
706C3×C4#52511yescharacteristic
707C3×C4#52511yescharacteristic
708Dic3—22no—
709Dic3—41no—
710Dic3—42no—
711Dic3—41no—
712Dic3—81no—
713Dic3—81no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—32no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—616no—
730C23—61no—
731C23—61no—
732C23—61no—
733C23—61no—
734C23—61no—
735C23—62no—
736C23—62no—
737C23—61no—
738C23—62no—
739C23—121no—
740C23—121no—
741C23—121no—
742C23—121no—
743C23—244no—
744C23—244no—
745C23—244no—
746C23—244no—
747C23—244no—
748C23—244no—
749C23C2×D3×D411yescharacteristic
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754D4—22no—
755D4—22no—
756D4—22no—
757D4—34no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—616no—
763D4—62no—
764D4—62no—
765D4—62no—
766D4—244no—
767D4#93814yes—
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—61no—
780C2×C4—61no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—62no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—84no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
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#93712yes—
805C2×C4#93712yes—
806C2×C4C2×D3×D411yescharacteristic
807C2×C4C2×D3×D411yescharacteristic
808C2×C4C2×#23711yescharacteristic
809C2×C4D3×#4111yescharacteristic
810C2×C4D3×#4111yescharacteristic
811C2×C4C22×#6711yescharacteristic
812C8—41no—
813C8—41no—
814C8—121no—
815C8—121no—
816C2×C3—44no—
817C2×C3—161no—
818C2×C3#284711yescharacteristic
819C2×C3#301211yescharacteristic
820C2×C3#301211yescharacteristic
821C2×C3#304111yescharacteristic
822C2×C3#304211yescharacteristic
823C2×C3#311811yescharacteristic
824C2×C3#311811yescharacteristic
825D3—42no—
826D3—44no—
827C22—24no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—62no—
835C22—64no—
836C22—62no—
837C22—62no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—121no—
846C22—122no—
847C22—121no—
848C22—122no—
849C22—122no—
850C22—122no—
851C22—122no—
852C22—121no—
853C22—122no—
854C22—121no—
855C22—2416no—
856C22D3×#12111yescharacteristic
857C22#560611yescharacteristic
858C22#576911yescharacteristic
859C22#577011yescharacteristic
860C22#577411yescharacteristic
861C22#577511yescharacteristic
862C22C2×#93711yescharacteristic
863C4—22no—
864C4—22no—
865C4—42no—
866C4—62no—
867C4—81no—
868C4—121no—
869C4—122no—
870C4—121no—
871C4—241no—
872C4—241no—
873C4D3×#12111yescharacteristic
874C4#560611yescharacteristic
875C4C2×#93811yescharacteristic
876C4#582811yescharacteristic
877C3#3291711yescharacteristic, complemented, Sylow
878C2—44no—
879C2—122no—
880C2—124no—
881C2—161no—
882C2#8050811yescharacteristic
883C2#8050911yescharacteristic
884C2#8053611yescharacteristic
885C2#8053711yescharacteristic
886C2#8272311yescharacteristic
887C2#8391211yescharacteristic
888C2#8394911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#463C2
socleC23×C3C22×D4
prime radicalC2×#5156C2
hypercenterC2×#463D3
hypocenterC3#32917
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#5545C2semidirect
2. C2×C3×#463C2semidirect
3. C2×#5169C2semidirect
5. #83001C2semidirect
6. C2×#5057C2semidirect
7. #72047C2semidirect
8. #72037C2semidirect
9. #71604C2semidirect
10. #70479C2semidirect
11. #70476C2semidirect
12. #70276C2semidirect
13. #70269C2semidirect
14. #70208C2semidirect
15. #70201C2semidirect
20. C2×C3×#124C22semidirect
38. C2×C3×C4⋊C8C22semidirect
39. C2×C3×#103C22semidirect
40. C2×C3×#102C22semidirect
41. #5229C22semidirect
42. C2×#835C22semidirect
43. #5221C22semidirect
46. C2×#832C22semidirect
58. #4935C22semidirect
59. C2×C4⋊(C3⋊C8)C22semidirect
60. #4551C22semidirect
61. #4551C22semidirect
62. #4550C22semidirect
63. #4550C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
68. C2×#463D3semidirect
110. C3×C4×D4D4semidirect
159. C4×D12D4semidirect
181. C2×#124C2×D3semidirect
201. C2×C4⋊C8C2×D3semidirect
203. C2×#103C2×D3semidirect
209. C2×#102C2×D3semidirect
395. C4×D4#67semidirect
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×C3×#4632
C2×#51692
C2×#51562
#830012
C2×#50572
#720472
#720372
#716042
#704792
#704762
#702762
#702692
#702082
#702012
#329173