Finite Group Databasebeta

← #10944097

Subgroups — #10944097

Order 768.

1546 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5545C211yesmaximal, characteristic
2C2×#5169C211yesmaximal, characteristic
3C2×#5162C211yesmaximal, characteristic, complemented
4C2×#4818C211yesmaximal, characteristic, complemented
5C2×#4776C211yesmaximal, characteristic
6#76641C211yesmaximal, characteristic, complemented
7C3×#1877C211yesmaximal, characteristic, complemented
8#71612C211yesmaximal, characteristic, complemented
9#70269C211yesmaximal, characteristic, complemented
10#70154C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#68893C211yesmaximal, characteristic, complemented
13#68879C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68663C211yesmaximal, characteristic, complemented
16#32914—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#944C2211yescharacteristic, complemented
22C22×#215C2211yescharacteristic
23C2×D4×Dic3C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C2×C4×#67—21no—
26C22×(C2×D3)⋊C4—21no—
27C22×#204C2211yescharacteristic
28#5545—24no—
29#5545—24no—
30C2×#897C2211yescharacteristic
31C2×#893C2211yescharacteristic
32C2×#892C2211yescharacteristic
33C2×#67⋊C4—21no—
34C2×D3×C22⋊C4—21no—
35C2×C4×D12C2211yescharacteristic
36C2×#872C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C3×#391C2211yescharacteristic, complemented
40C2×#835C2211yescharacteristic, complemented
41C2×#832C2211yescharacteristic
42#5169—24no—
43#5162—24no—
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#816C2211yescharacteristic, complemented
48C2×Dic3⋊C8C2211yescharacteristic, complemented
49C2×Dic3⋊C8C2211yescharacteristic, complemented
50#4977C2211yescharacteristic, complemented
51C2×#810C2211yescharacteristic, complemented
52C2×#809C2211yescharacteristic
53#4929C2211yescharacteristic, complemented
54#4818—24no—
55#4776—24no—
56#4675—21no—
57#4675—21no—
58#4657—21no—
59#4657—21no—
60C3×#340C2211yescharacteristic, complemented
61C3×#336C2211yescharacteristic, complemented
62#4551C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4524C2211yescharacteristic, complemented
66C2×#518—31no—
67C2×#461—31no—
68C2×#461—31no—
69C2×#450—31no—
70C2×#450—31no—
71#2621—31no—
72#1877—31no—
73#1877—31no—
74#1877—31no—
75#1877D311yescharacteristic, complemented
76#1873—31no—
77#1873—31no—
78#1804—31no—
79#1804—31no—
80#1798—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4D414yes—
93C22×D12C2311yescharacteristic
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3C2311yescharacteristic
97C22×Dic6C2311yescharacteristic
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×C4×D4—22no—
104C3×C4×D4—22no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C42C2311yescharacteristic
109C2×#217—21no—
110#946—22no—
111#946—22no—
112#944—22no—
113#944—22no—
114C2×#215—22no—
115C2×#215—22no—
116C2×#215—22no—
117D4×Dic3—22no—
118D4×Dic3D414yes—
119C2×#214—22no—
120C2×#214—22no—
121C2×#214—22no—
122C4×#67—28no—
123C2×(C2×D3)⋊C4—28no—
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)⋊C4D411yescharacteristic
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4D411yescharacteristic
138C2×Dic3⋊C4D411yescharacteristic
139C2×C4×Dic3—21no—
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×#204—22no—
144C2×#204—22no—
145C2×#204—22no—
146#897—22no—
147#897—22no—
148#893—22no—
149#893D414yes—
150#892—22no—
151#892—22no—
152#67⋊C4—28no—
153D3×C22⋊C4—28no—
154C4×D12—22no—
155C4×D12—22no—
156#872—22no—
157#872—22no—
158C3×#103—22no—
159C3×#102—22no—
160C3×#95—21no—
161C3×#95—21no—
162#835—22no—
163#832—22no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#821—22no—
169(C2×D3)⋊C8—22no—
170(C2×D3)⋊C8—22no—
171#816—22no—
172Dic3⋊C8—22no—
173Dic3⋊C8—22no—
174#810—22no—
175#809—22no—
176C23×D4—31no—
177C22×SD16—31no—
178C22×SD16—31no—
179C22×SD16—31no—
180C22×SD16C2×D311yescharacteristic
181C2×C4⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—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#461—64no—
197#461—64no—
198#450—64no—
199#450—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103C2×D311yescharacteristic, complemented
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212#398—61no—
213#398—61no—
214#397—61no—
215#397—61no—
216#391—31no—
217#391C2×D311yescharacteristic, complemented
218#382—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340C2×D311yescharacteristic, complemented
223#336—31no—
224#336C2×D311yescharacteristic, complemented
225C24×C3—21no—
226C23×D3—21no—
227C23×D3—24no—
228C23×D3—24no—
229C23×D3—24no—
230C23×D3—81no—
231C23×D3—81no—
232C23×D3—81no—
233C23×D3—81no—
234C23×D3C2×D411yescharacteristic
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4C2×D412yes—
245C2×C3×D4C2×D412yes—
246C2×C3×D4#4112yes—
247C22×C3×C4—21no—
248C22×C3×C4—24no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—81no—
252C22×C3×C4—81no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2411yescharacteristic
256C2×#67—24no—
257C2×#67—24no—
258C2×#67—24no—
259C22×Dic3—21no—
260C22×Dic3—24no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—81no—
264C22×Dic3—81no—
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267C22×Dic3C2×D411yescharacteristic
268D3×D4—28no—
269D3×D4—28no—
270D3×D4—28no—
271D3×D4—28no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12C2×D412yes—
276C2×D12C2×D412yes—
277C2×D12#4112yes—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—24no—
283C2×C4×D3—24no—
284C2×C4×D3—81no—
285C2×C4×D3—81no—
286C2×C4×D3—81no—
287C2×C4×D3—81no—
288C2×C4×D3C2×D412yes—
289C2×C4×D3#4112yes—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C3×SD16—44no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4C2×D412yes—
307C3×C22⋊C4—24no—
308C3×C42—21no—
309C3×C42—21no—
310#217—24no—
311#215—44no—
312#214—44no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—24no—
315(C2×D3)⋊C4—22no—
316(C2×D3)⋊C4—22no—
317(C2×D3)⋊C4—24no—
318(C2×D3)⋊C4—42no—
319(C2×D3)⋊C4—42no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3—42no—
324C4⋊Dic3C2×D412yes—
325Dic3⋊C4—22no—
326Dic3⋊C4—22no—
327Dic3⋊C4—42no—
328Dic3⋊C4—42no—
329Dic3⋊C4—42no—
330C4×Dic3—24no—
331C4×Dic3C2×D412yes—
332C4×Dic3C2×D412yes—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339#204—44no—
340C25—61no—
341C22×Q8—31no—
342C22×Q8C22×D311yescharacteristic
343C22×D4—34no—
344C22×D4—31no—
345C22×D4—62no—
346C22×D4—61no—
347C22×D4—62no—
348C22×D4—62no—
349C22×D4—62no—
350C22×D4—62no—
351C22×D4C22×D311yescharacteristic
352C23×C4—21no—
353C23×C4—31no—
354C23×C4—61no—
355C23×C4—61no—
356C23×C4—61no—
357C2×SD16—22no—
358C2×SD16—22no—
359C2×SD16—22no—
360C2×SD16—62no—
361C2×SD16—62no—
362C2×SD16—62no—
363C2×SD16—62no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×SD16—62no—
367C2×SD16—62no—
368C2×SD16—62no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8C22×D311yescharacteristic
372C22×C8C22×D311yescharacteristic
373C4⋊Q8—62no—
374C4⋊Q8—62no—
375C22⋊Q8—62no—
376C22⋊Q8—62no—
377C22⋊Q8—62no—
378C22⋊Q8—62no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—34no—
382C4×D4—34no—
383C4×D4—62no—
384C4×D4—62no—
385C4×D4—62no—
386C4×D4—62no—
387C4×D4—68no—
388C4×D4—68no—
389#117—62no—
390#117—62no—
391#117—62no—
392#117—62no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4—61no—
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C4⋊C4C22×D311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—68no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C22⋊C4—68no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C42—31no—
415C2×C42—61no—
416C2×C42C22×D311yescharacteristic
417C4⋊C8—62no—
418C4⋊C8—62no—
419#103—22no—
420#103—62no—
421#103—62no—
422#103—62no—
423#102—22no—
424#102—62no—
425#102—62no—
426#102—62no—
427C22⋊C8—62no—
428C22⋊C8—62no—
429#95—21no—
430#95—21no—
431#95—61no—
432#95—61no—
433#95—61no—
434#95—61no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3C22×D411yescharacteristic
443C22×D3—21no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—21no—
447C22×D3—22no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—216no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C22×D3—84no—
458C22×D3—84no—
459C22×D3—84no—
460C22×D3—84no—
461C22×D3—84no—
462C22×D3—84no—
463C22×D3#12112yes—
464C3×Q8—41no—
465C3×Q8—41no—
466C3×Q8—41no—
467C3×Q8—41no—
468C3×D4—22no—
469C3×D4—22no—
470C3×D4—22no—
471C3×D4#12114yes—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
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×C4—84no—
488C2×C3×C4C22×D411yescharacteristic
489C2×C3×C4C22×D411yescharacteristic
490C2×C3×C4C22×D411yescharacteristic
491C2×C3×C4C2×#4111yescharacteristic
492C2×C3×C4C2×#4111yescharacteristic
493C2×C3×C4C2×#4111yescharacteristic
494#67—216no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—22no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—84no—
511C2×Dic3#12012yes—
512C2×Dic3#12012yes—
513C2×Dic3#12112yes—
514D12—22no—
515D12—22no—
516D12—22no—
517D12#12114yes—
518C4×D3—22no—
519C4×D3—22no—
520C4×D3—22no—
521C4×D3—22no—
522C4×D3—84no—
523C4×D3—84no—
524Dic6—41no—
525Dic6—41no—
526Dic6—41no—
527Dic6—41no—
528C3×C8—41no—
529C3×C8—41no—
530C3⋊C8—41no—
531C3⋊C8—41no—
532C24—21no—
533C24—31no—
534C24—64no—
535C24—64no—
536C24—64no—
537C24—61no—
538C24—241no—
539C24—241no—
540C24—241no—
541C24—241no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—61no—
549C2×Q8—61no—
550C2×Q8—61no—
551C2×Q8—61no—
552C2×Q8—61no—
553C2×Q8—61no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—32no—
558C2×D4—32no—
559C2×D4—32no—
560C2×D4—64no—
561C2×D4—68no—
562C2×D4—68no—
563C2×D4—68no—
564C2×D4—64no—
565C2×D4—64no—
566C2×D4—68no—
567C2×D4—61no—
568C2×D4—61no—
569C2×D4—61no—
570C2×D4#23512yes—
571C2×D4D3×D412yes—
572C2×D4D3×D412yes—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—32no—
581C22×C4—32no—
582C22×C4—64no—
583C22×C4—64no—
584C22×C4—64no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—81no—
593C22×C4—81no—
594C22×C4—241no—
595C22×C4—241no—
596C22×C4—241no—
597C22×C4—241no—
598C22×C4—241no—
599C22×C4—241no—
600C22×C4D3×D411yescharacteristic
601C22×C4D3×D411yescharacteristic
602C22×C4C23×D311yescharacteristic
603SD16—44no—
604SD16—124no—
605SD16—124no—
606SD16—124no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—61no—
614C2×C8—61no—
615C2×C8—61no—
616C2×C8—61no—
617C2×C8—61no—
618C2×C8—61no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—32no—
623C4⋊C4—62no—
624C4⋊C4—62no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—122no—
629C4⋊C4—122no—
630C4⋊C4—122no—
631C4⋊C4—122no—
632C4⋊C4D3×D412yes—
633C22⋊C4—24no—
634C22⋊C4—62no—
635C22⋊C4—62no—
636C22⋊C4—64no—
637C22⋊C4—64no—
638C22⋊C4—64no—
639C22⋊C4—64no—
640C22⋊C4—122no—
641C22⋊C4—122no—
642C42—21no—
643C42—21no—
644C42—32no—
645C42—32no—
646C42—64no—
647C22×C3—24no—
648C22×C3—42no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3C2×#12011yescharacteristic
655C22×C3C2×#12111yescharacteristic
656C22×C3#52511yescharacteristic
657C22×C3#57711yescharacteristic
658C22×C3#57711yescharacteristic
659C22×C3#57711yescharacteristic
660C22×C3#57711yescharacteristic
661C2×D3—22no—
662C2×D3—24no—
663C2×D3—22no—
664C2×D3—22no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—42no—
668C2×D3—42no—
669C2×D3—42no—
670C2×D3—42no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—816no—
676C3×C4—41no—
677C3×C4—42no—
678C3×C4—41no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4C2×#12111yescharacteristic
682C3×C4C2×#12111yescharacteristic
683C3×C4#52511yescharacteristic
684C3×C4#52511yescharacteristic
685Dic3—22no—
686Dic3—22no—
687Dic3—22no—
688Dic3—42no—
689Dic3—81no—
690Dic3—81no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—32no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—616no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—62no—
706C23—61no—
707C23—62no—
708C23—62no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—244no—
714C23—244no—
715C23—244no—
716C23—244no—
717C23—244no—
718C23—244no—
719C23C2×D3×D411yescharacteristic
720Q8—41no—
721Q8—41no—
722Q8—41no—
723Q8—41no—
724Q8—121no—
725Q8—121no—
726Q8—121no—
727Q8—121no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—34no—
732D4—616no—
733D4—62no—
734D4—62no—
735D4—62no—
736D4#88414yes—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—32no—
745C2×C4—32no—
746C2×C4—32no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—84no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4—121no—
775C2×C4—244no—
776C2×C4—244no—
777C2×C4—244no—
778C2×C4C2×#23511yescharacteristic
779C2×C4C2×D3×D411yescharacteristic
780C2×C4C2×D3×D411yescharacteristic
781C2×C4C2×D3×D411yescharacteristic
782C2×C4D3×#4111yescharacteristic
783C2×C4D3×#4111yescharacteristic
784C8—41no—
785C8—41no—
786C8—121no—
787C8—121no—
788C2×C3—44no—
789C2×C3#284711yescharacteristic
790C2×C3#300911yescharacteristic
791C2×C3#300911yescharacteristic
792C2×C3#304211yescharacteristic
793C2×C3#304211yescharacteristic
794C2×C3#312311yescharacteristic
795C2×C3#312311yescharacteristic
796D3—42no—
797D3—44no—
798C22—24no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—62no—
806C22—62no—
807C22—62no—
808C22—64no—
809C22—122no—
810C22—121no—
811C22—121no—
812C22—122no—
813C22—122no—
814C22—122no—
815C22—121no—
816C22—122no—
817C22—121no—
818C22—122no—
819C22—2416no—
820C22#554711yescharacteristic
821C22D3×#12011yescharacteristic
822C22D3×#12111yescharacteristic
823C22#576211yescharacteristic
824C22#577011yescharacteristic
825C22#577511yescharacteristic
826C22#577811yescharacteristic
827C4—41no—
828C4—42no—
829C4—41no—
830C4—62no—
831C4—62no—
832C4—62no—
833C4—81no—
834C4—81no—
835C4—122no—
836C4—241no—
837C4—241no—
838C4C2×#88411yescharacteristic
839C4#554711yescharacteristic
840C4D3×#12111yescharacteristic
841C4#565611yescharacteristic
842C3#3291411yescharacteristic, complemented, Sylow
843C2—44no—
844C2—122no—
845C2—124no—
846C2#7493511yescharacteristic
847C2#7965911yescharacteristic
848C2#7978711yescharacteristic
849C2#8014811yescharacteristic
850C2#8022911yescharacteristic
851C2#8043011yescharacteristic
852C2#8053711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1877C2
socleC23×C3C22×D4
prime radicalC22×D3×D4C22
hypercenter#1877D3
hypocenterC3#32914
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
3. C2×#5162C2semidirect
4. C2×#4818C2semidirect
6. #76641C2semidirect
7. C3×#1877C2semidirect
8. #71612C2semidirect
9. #70269C2semidirect
10. #70154C2semidirect
11. #69687C2semidirect
12. #68893C2semidirect
13. #68879C2semidirect
14. #68672C2semidirect
15. #68663C2semidirect
21. C2×#944C22semidirect
37. C2×C3×#103C22semidirect
39. C3×#391C22semidirect
40. C2×#835C22semidirect
47. C2×#816C22semidirect
48. C2×Dic3⋊C8C22semidirect
49. C2×Dic3⋊C8C22semidirect
50. #4977C22semidirect
51. C2×#810C22semidirect
53. #4929C22semidirect
60. C3×#340C22semidirect
61. C3×#336C22semidirect
62. #4551C22semidirect
63. #4529C22semidirect
64. #4529C22semidirect
65. #4524C22semidirect
75. #1877D3semidirect
205. C2×#103C2×D3semidirect
217. #391C2×D3semidirect
222. #340C2×D3semidirect
224. #336C2×D3semidirect
842. C3#32914semidirect

Maximal subgroups

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

subgroupindex
C2×#55452
C2×#51692
C2×#51622
C2×#48182
C2×#47762
#766412
C3×#18772
#716122
#702692
#701542
#696872
#688932
#688792
#686722
#686632
#329143