Finite Group Databasebeta

← #10833363

Subgroups — #10833363

Order 768.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3489C211yesmaximal, characteristic, complemented
2C2×#5245C211yesmaximal, characteristic, complemented
3#84082C211yesmaximal, characteristic, complemented
4C22×#837C211yesmaximal, characteristic, complemented
5#82924C211yesmaximal, characteristic, complemented
6#82809C211yesmaximal, characteristic, complemented
7#72143C211yesmaximal, characteristic, complemented
8#71879C211yesmaximal, characteristic, complemented
9#71877C211yesmaximal, characteristic, complemented
10#71867C211yesmaximal, characteristic, complemented
11#71863C211yesmaximal, characteristic, complemented
12#71711C211yesmaximal, characteristic, complemented
13#71698C211yesmaximal, characteristic, complemented
14#71667C211yesmaximal, characteristic, complemented
15#71665C211yesmaximal, characteristic, complemented
16#24465—31nomaximal, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C3×D4×Q8—21no—
20C3×#548—21no—
21C3×#547—21no—
22C3×#547—22no—
23C3×#546—21no—
24C3×#546—22no—
25C3×#537—21no—
26C3×#537C2211yescharacteristic
27C3×#536—21no—
28C3×#536C2211yescharacteristic
29C3×#525—21no—
30C3×#525C2211yescharacteristic
31C2×C3×C22⋊Q8—21no—
32C2×C3×C22⋊Q8C2211yescharacteristic
33C3×#520C2211yescharacteristic
34C2×#949C2211yescharacteristic
35C2×#949C2211yescharacteristic
36C2×#949C2211yescharacteristic, complemented
37C2×#947C2211yescharacteristic, complemented
38C2×#930C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C22×#208C2211yescharacteristic
41#5245—24no—
42#5238—21no—
43#5238—21no—
44C2×#837—24no—
45C2×#837C2211yescharacteristic
46C2×#837C2211yescharacteristic
47C2×#837C2211yescharacteristic
48C2×#837C2211yescharacteristic
49C2×#837C2211yescharacteristic, complemented
50C2×#837C2211yescharacteristic, complemented
51#5232C2211yescharacteristic
52#5232C2211yescharacteristic
53#5232C2211yescharacteristic, complemented
54#5229C2211yescharacteristic, complemented
55#5227—21no—
56C2×#836C2211yescharacteristic, complemented
57C2×#836C2211yescharacteristic, complemented
58#5217—21no—
59#5207C2211yescharacteristic
60#5049—21no—
61#5048—21no—
62#5039—21no—
63#5038—21no—
64#5001C2211yescharacteristic, complemented
65#4995C2211yescharacteristic, complemented
66#4990—22no—
67#4988C2211yescharacteristic, complemented
68#4977C2211yescharacteristic, complemented
69#4958—22no—
70#4532C2211yescharacteristic, complemented
71#4532C2211yescharacteristic, complemented
72#4530C2211yescharacteristic, complemented
73#4530C2211yescharacteristic, complemented
74#3489D311yescharacteristic, complemented
75#3055—31no—
76C2×#454—31no—
77#3006—31no—
78C22×#104—31no—
79#2850—31no—
80#2040—31no—
81#2038—31no—
82#2006—31no—
83#2003—31no—
84#1901—31no—
85#1896—31no—
86#1883—31no—
87#1860—31no—
88#1793—31no—
89C3×2−1+4—22no—
90C3×2−1+4—22no—
91C3×2−1+4—41no—
92C3×2−1+4—41no—
93C2×C3×#41—21no—
94C2×C3×#41—21no—
95C2×C3×#41—21no—
96C2×C3×#41—21no—
97C2×C3×#41—22no—
98C2×C3×#41—22no—
99C2×C3×#41—22no—
100C2×C3×#41—41no—
101C2×C3×#41—41no—
102C2×C3×#41D411yescharacteristic
103C2×C3×#41D411yescharacteristic
104C2×C3×#41C2311yescharacteristic
105C2×C3×#41C2311yescharacteristic
106C2×C3×#41C2311yescharacteristic
107C22×C3×Q8—21no—
108C22×C3×Q8—21no—
109C22×C3×Q8D411yescharacteristic
110C22×C3×Q8C2311yescharacteristic
111C22×C3×D4—21no—
112C22×C3×D4D411yescharacteristic
113C23×C3×C4—21no—
114C23×C3×C4C2311yescharacteristic
115C22×#67—21no—
116C23×Dic3—21no—
117C22×D12C2311yescharacteristic
118C3×C4⋊Q8—22no—
119C3×C4⋊Q8—21no—
120C3×#124—22no—
121C3×#124—21no—
122C3×#123—22no—
123C3×#123—22no—
124C3×#123—22no—
125C3×#123—21no—
126C3×#123—22no—
127C3×C22⋊Q8—22no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—22no—
130C3×C22⋊Q8—21no—
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8—21no—
133C3×C22⋊Q8—21no—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8—21no—
136C3×C22⋊Q8—21no—
137C3×C22⋊Q8—21no—
138C3×C22⋊Q8D411yescharacteristic
139C3×C22⋊Q8D411yescharacteristic
140C3×#121—22no—
141C3×#121—22no—
142C3×#121—22no—
143C3×#121—21no—
144C3×#121—21no—
145C3×#121—22no—
146C3×#121D411yescharacteristic
147C3×#121D411yescharacteristic
148C3×#120—22no—
149C3×#120—21no—
150C3×C4×Q8—21no—
151C3×C4×D4—22no—
152C3×C4×D4—22no—
153C3×C4×D4—21no—
154C3×C4×D4—22no—
155C3×C4×D4—21no—
156C3×C4×D4—21no—
157C3×#117—21no—
158C3×#117C2311yescharacteristic
159C2×C3×C4⋊C4—22no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4D412yes—
162C2×C3×C4⋊C4C2311yescharacteristic
163C2×C3×C22⋊C4—22no—
164C2×C3×C22⋊C4D412yes—
165#949—22no—
166#949—22no—
167#949—22no—
168#949—41no—
169#949—41no—
170#949—41no—
171#947—22no—
172#947—41no—
173C2×#215—21no—
174C2×#215—21no—
175C2×#215—21no—
176C2×#213—21no—
177C2×#213—21no—
178C2×#213—21no—
179#930—21no—
180#930—21no—
181#930—21no—
182#930—21no—
183C2×(C2×D3)⋊C4—22no—
184C2×(C2×D3)⋊C4—22no—
185C2×(C2×D3)⋊C4—21no—
186C2×C4⋊Dic3C2311yescharacteristic
187C2×C4×Dic3—22no—
188C2×C4×Dic3—21no—
189C2×C4×Dic3—41no—
190C2×C4×Dic3C2311yescharacteristic
191C2×C4×Dic3C2311yescharacteristic
192C2×#208—21no—
193C2×#208—22no—
194C2×#208—41no—
195C2×#208C2311yescharacteristic
196C2×#208C2311yescharacteristic
197C2×#208C2311yescharacteristic
198C2×#208C2311yescharacteristic
199C22×C3⋊C8—21no—
200#837—22no—
201#837—22no—
202#837—22no—
203#837—22no—
204#837—41no—
205#837D414yescomplemented
206#836—22no—
207#836—41no—
208#835—21no—
209#835—21no—
210#835—21no—
211#832—21no—
212#832—21no—
213#832—21no—
214C3⋊#95—22no—
215C3⋊#95—22no—
216#830—21no—
217#830—21no—
218#809—21no—
219#809—21no—
220#808—21no—
221#807—21no—
222C2×2−1+4C2×D311yescharacteristic
223C22×#41C2×D311yescharacteristic
224C2×AGL(1,ℤ/8)—31no—
225C2×AGL(1,ℤ/8)—31no—
226C2×AGL(1,ℤ/8)—31no—
227C22×M16—31no—
228D4×Q8—21no—
229#548—21no—
230#547—21no—
231#547—22no—
232#546—21no—
233#546—22no—
234#537—21no—
235#537C2×D311yescharacteristic
236#536—21no—
237#536C2×D311yescharacteristic
238C2×#124—31no—
239#525—21no—
240#525C2×D311yescharacteristic
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8C2×D311yescharacteristic
243C2×#121—31no—
244#520C2×D311yescharacteristic
245C22×C42—31no—
246#469—61no—
247#468—61no—
248#466—61no—
249#465—61no—
250#454—64no—
251#449—61no—
252#449—61no—
253#448—61no—
254#447—61no—
255#428—31no—
256C2×#104—31no—
257C2×#104—31no—
258C2×#104—31no—
259C2×#104—31no—
260C2×#104—31no—
261C2×#104—31no—
262C2×#104—64no—
263#418—31no—
264#417—31no—
265#417—31no—
266#417—31no—
267C2×#101—31no—
268C2×#101—31no—
269#407—31no—
270#391—31no—
271#390—31no—
272#388—62no—
273#386—62no—
274#382—31no—
275#343—31no—
276#343—31no—
277#339—31no—
278#339—31no—
279C24×C3—21no—
280C24×C3C2×D411yescharacteristic
281C23×D3—21no—
282C3×#41—21no—
283C3×#41—21no—
284C3×#41—22no—
285C3×#41—22no—
286C3×#41—21no—
287C3×#41—21no—
288C3×#41—21no—
289C3×#41—21no—
290C3×#41—21no—
291C3×#41—21no—
292C3×#41—21no—
293C3×#41—21no—
294C3×#41—42no—
295C3×#41—42no—
296C3×#41—41no—
297C3×#41—41no—
298C3×#41—42no—
299C3×#41—42no—
300C3×#41—42no—
301C3×#41—42no—
302C3×#41—44no—
303C3×#41—44no—
304C3×#41—42no—
305C3×#41—42no—
306C3×#41C2×D412yes—
307C3×#41#4112yes—
308C2×C3×Q8—22no—
309C2×C3×Q8—21no—
310C2×C3×Q8—21no—
311C2×C3×Q8—21no—
312C2×C3×Q8—21no—
313C2×C3×Q8—21no—
314C2×C3×Q8—21no—
315C2×C3×Q8—21no—
316C2×C3×Q8—22no—
317C2×C3×Q8—41no—
318C2×C3×Q8—42no—
319C2×C3×Q8—42no—
320C2×C3×Q8—42no—
321C2×C3×Q8—42no—
322C2×C3×Q8C2×D411yescharacteristic
323C2×C3×Q8C2×D411yescharacteristic
324C2×C3×Q8C2×D411yescharacteristic
325C2×C3×D4—21no—
326C2×C3×D4—22no—
327C2×C3×D4—22no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—22no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—41no—
337C2×C3×D4—42no—
338C2×C3×D4—42no—
339C2×C3×D4C2×D411yescharacteristic
340C2×C3×D4C2×D411yescharacteristic
341C2×C3×D4C2×D411yescharacteristic
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—22no—
348C22×C3×C4—22no—
349C22×C3×C4—21no—
350C22×C3×C4—22no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—42no—
356C22×C3×C4—42no—
357C22×C3×C4C2×D412yes—
358C22×C3×C4C2×D411yescharacteristic
359C22×C3×C4C2×D411yescharacteristic
360C22×C3×C4C2×D411yescharacteristic
361C22×C3×C4C2×D411yescharacteristic
362C22×C3×C4C2×D411yescharacteristic
363C22×C3×C4C2×D412yes—
364C22×C3×C4C2411yescharacteristic
365C2×#67—44no—
366C2×#67—41no—
367C2×#67—41no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—42no—
372C22×Dic3—42no—
373C22×Dic3—42no—
374C2×D12—21no—
375C2×D12—21no—
376C2×D12—21no—
377C2×D12—21no—
378C2×D12—21no—
379C2×D12—21no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—22no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—22no—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4C2×D411yescharacteristic
391C3×C4⋊C4C2×D411yescharacteristic
392C3×C22⋊C4—22no—
393C3×C22⋊C4—22no—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—22no—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—21no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—21no—
404C3×C42—22no—
405C3×C42—21no—
406#215—42no—
407#215—42no—
408#215—42no—
409#213—42no—
410#213—42no—
411#213—42no—
412(C2×D3)⋊C4—44no—
413(C2×D3)⋊C4—44no—
414(C2×D3)⋊C4—41no—
415(C2×D3)⋊C4—41no—
416C4⋊Dic3—21no—
417C4⋊Dic3—21no—
418C4×Dic3—21no—
419C4×Dic3—21no—
420C4×Dic3—21no—
421C4×Dic3—42no—
422C4×Dic3C2×D412yes—
423#208—21no—
424#208—21no—
425#208—21no—
426#208—21no—
427#208—21no—
428#208—21no—
429#208—21no—
430#208—42no—
431#208C2×D412yes—
432C2×C3⋊C8—21no—
433C2×C3⋊C8—21no—
434C2×C3⋊C8—21no—
435C2×C3⋊C8—21no—
436C2×C3⋊C8—42no—
4372−1+4—22no—
4382−1+4—22no—
4392−1+4—41no—
4402−1+4—41no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—22no—
445C2×#41—21no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—41no—
449C2×#41—41no—
450C2×#41#6711yescharacteristic
451C2×#41#6711yescharacteristic
452C2×#41C22×D311yescharacteristic
453C2×#41C22×D311yescharacteristic
454C2×#41C22×D311yescharacteristic
455C22×Q8—21no—
456C22×Q8—21no—
457C22×Q8#6711yescharacteristic
458C22×Q8C22×D311yescharacteristic
459C22×D4—21no—
460C22×D4—31no—
461C22×D4—61no—
462C22×D4#6711yescharacteristic
463C23×C4—21no—
464C23×C4—61no—
465C23×C4C22×D311yescharacteristic
466AGL(1,ℤ/8)—62no—
467AGL(1,ℤ/8)—62no—
468AGL(1,ℤ/8)—62no—
469AGL(1,ℤ/8)—121no—
470AGL(1,ℤ/8)—121no—
471AGL(1,ℤ/8)—121no—
472C2×SD16—61no—
473C2×SD16—61no—
474C2×SD16—61no—
475C2×D8—61no—
476C2×D8—61no—
477C2×D8—61no—
478C2×M16—31no—
479C2×M16—31no—
480C2×M16—31no—
481C2×M16—31no—
482C2×M16—61no—
483C2×M16—62no—
484C2×M16—121no—
485C22×C8—61no—
486C4⋊Q8—22no—
487C4⋊Q8—21no—
488#124—22no—
489#124—21no—
490#124—62no—
491#124—121no—
492#123—22no—
493#123—22no—
494#123—22no—
495#123—21no—
496#123—22no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508C22⋊Q8#6711yescharacteristic
509C22⋊Q8#6711yescharacteristic
510#121—22no—
511#121—22no—
512#121—22no—
513#121—21no—
514#121—21no—
515#121—22no—
516#121—61no—
517#121—61no—
518#121—61no—
519#121—61no—
520#121#6711yescharacteristic
521#121#6711yescharacteristic
522#120—22no—
523#120—21no—
524C4×Q8—21no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—22no—
529C4×D4—21no—
530C4×D4—21no—
531#117—21no—
532#117C22×D311yescharacteristic
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4#6712yes—
537C2×C4⋊C4C22×D311yescharacteristic
538C2×C22⋊C4—22no—
539C2×C22⋊C4—61no—
540C2×C22⋊C4—62no—
541C2×C22⋊C4—62no—
542C2×C22⋊C4#6712yes—
543C2×C42—31no—
544C2×C42—31no—
545C2×C42—62no—
546C2×C42—61no—
547C2×C42—121no—
548#107—61no—
549#106—61no—
550#104—34no—
551#104—62no—
552#104—62no—
553#104—62no—
554#104—62no—
555#104—121no—
556#103—61no—
557#103—61no—
558#103—61no—
559#102—61no—
560#102—61no—
561#102—61no—
562#102—61no—
563#102—61no—
564#101—62no—
565#101—121no—
566C22⋊C8—61no—
567C22⋊C8—61no—
568#95—62no—
569#95—62no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—22no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—41no—
577C23×C3—42no—
578C23×C3—42no—
579C23×C3—81no—
580C23×C3#12011yescharacteristic
581C23×C3#12011yescharacteristic
582C23×C3C22×D411yescharacteristic
583C22×D3—42no—
584C22×D3—42no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C3×Q8—21no—
589C3×Q8—21no—
590C3×Q8—21no—
591C3×Q8—21no—
592C3×Q8—21no—
593C3×Q8—42no—
594C3×Q8—44no—
595C3×Q8—41no—
596C3×Q8—41no—
597C3×Q8—41no—
598C3×Q8—41no—
599C3×Q8#12112yes—
600C3×D4—22no—
601C3×D4—22no—
602C3×D4—21no—
603C3×D4—21no—
604C3×D4—21no—
605C3×D4—21no—
606C3×D4—21no—
607C3×D4—42no—
608C3×D4—42no—
609C3×D4—42no—
610C3×D4—44no—
611C3×D4—41no—
612C3×D4—41no—
613C3×D4—41no—
614C3×D4—41no—
615C3×D4—42no—
616C3×D4—81no—
617C3×D4—82no—
618C3×D4#12112yes—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—22no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—22no—
632C2×C3×C4—21no—
633C2×C3×C4—22no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—22no—
637C2×C3×C4—21no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—42no—
641C2×C3×C4—42no—
642C2×C3×C4—42no—
643C2×C3×C4—44no—
644C2×C3×C4—44no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—42no—
650C2×C3×C4—82no—
651C2×C3×C4#12011yescharacteristic
652C2×C3×C4#12011yescharacteristic
653C2×C3×C4C22×D411yescharacteristic
654C2×C3×C4C22×D411yescharacteristic
655C2×C3×C4C22×D411yescharacteristic
656C2×C3×C4C2×#4111yescharacteristic
657C2×C3×C4H(5,𝔽2)11yescharacteristic
658C2×C3×C4H(5,𝔽2)11yescharacteristic
659#67—82no—
660#67—82no—
661C2×Dic3—22no—
662C2×Dic3—22no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—48no—
667C2×Dic3—41no—
668C2×Dic3—42no—
669C2×Dic3—41no—
670D12—41no—
671D12—41no—
672D12—41no—
673D12—41no—
674C3⋊C8—22no—
675C3⋊C8—41no—
676C3⋊C8—41no—
677C3⋊C8—41no—
678C24—21no—
679C24—61no—
680C24C2×#6711yescharacteristic
681#41—21no—
682#41—21no—
683#41—22no—
684#41—22no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—21no—
689#41—21no—
690#41—21no—
691#41—21no—
692#41—21no—
693#41—42no—
694#41—42no—
695#41—41no—
696#41—41no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41—42no—
701#41—44no—
702#41—44no—
703#41—42no—
704#41—42no—
705#41D3×D412yes—
706#41#23712yes—
707C2×Q8—22no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—22no—
716C2×Q8—41no—
717C2×Q8—42no—
718C2×Q8—42no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8C2×#6711yescharacteristic
722C2×Q8C2×#6711yescharacteristic
723C2×Q8C2×#6711yescharacteristic
724C2×D4—21no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—41no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—61no—
739C2×D4—61no—
740C2×D4—61no—
741C2×D4—61no—
742C2×D4—61no—
743C2×D4—61no—
744C2×D4—124no—
745C2×D4—121no—
746C2×D4—121no—
747C2×D4C2×#6711yescharacteristic
748C2×D4C2×#6711yescharacteristic
749C2×D4C2×#6711yescharacteristic
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—122no—
769C22×C4—122no—
770C22×C4—122no—
771C22×C4C2×#6712yes—
772C22×C4C2×#6711yescharacteristic
773C22×C4C2×#6711yescharacteristic
774C22×C4C2×#6711yescharacteristic
775C22×C4C2×#6711yescharacteristic
776C22×C4C2×#6711yescharacteristic
777C22×C4C2×#6712yes—
778C22×C4C23×D311yescharacteristic
779SD16—122no—
780SD16—122no—
781SD16—122no—
782D8—122no—
783D8—122no—
784D8—122no—
785M16—32no—
786M16—61no—
787M16—61no—
788M16—61no—
789M16—61no—
790M16—61no—
791M16—61no—
792M16—61no—
793M16—122no—
794C2×C8—61no—
795C2×C8—61no—
796C2×C8—61no—
797C2×C8—61no—
798C2×C8—122no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—61no—
810C4⋊C4—61no—
811C4⋊C4C2×#6711yescharacteristic
812C4⋊C4C2×#6711yescharacteristic
813C22⋊C4—22no—
814C22⋊C4—22no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—22no—
818C22⋊C4—21no—
819C22⋊C4—22no—
820C22⋊C4—22no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—124no—
826C22⋊C4—124no—
827C22⋊C4—121no—
828C22⋊C4—121no—
829C42—22no—
830C42—21no—
831C42—32no—
832C42—61no—
833C42—61no—
834C42—61no—
835C42—122no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—22no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—84no—
855C22×C3#45412yescomplemented
856C22×C3C2×#12011yescharacteristic
857C22×C3D4211yescharacteristic
858C22×C3#54611yescharacteristic
859C2×D3—82no—
860C2×D3—82no—
861C2×D3—81no—
862C2×D3—81no—
863C2×D3—81no—
864C3×C4—21no—
865C3×C4—21no—
866C3×C4—22no—
867C3×C4—42no—
868C3×C4—41no—
869C3×C4—41no—
870C3×C4—41no—
871C3×C4—42no—
872C3×C4—41no—
873C3×C4C2×#12111yescharacteristic
874C3×C4#53411yescharacteristic
875C3×C4D4211yescharacteristic
876C3×C4#54611yescharacteristic
877Dic3—42no—
878Dic3—42no—
879Dic3—81no—
880C23—22no—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—41no—
887C23—42no—
888C23—42no—
889C23—81no—
890C23—122no—
891C23—122no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23#95311yescharacteristic
896C23#95311yescharacteristic
897C23C22×#6711yescharacteristic
898Q8—21no—
899Q8—21no—
900Q8—21no—
901Q8—21no—
902Q8—21no—
903Q8—42no—
904Q8—44no—
905Q8—41no—
906Q8—41no—
907Q8—41no—
908Q8—41no—
909Q8#93912yes—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—42no—
918D4—42no—
919D4—42no—
920D4—44no—
921D4—42no—
922D4—41no—
923D4—41no—
924D4—41no—
925D4—41no—
926D4—81no—
927D4—82no—
928D4—121no—
929D4—121no—
930D4—121no—
931D4—121no—
932D4—242no—
933D4—242no—
934D4#93912yes—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—21no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—44no—
960C2×C4—44no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—42no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—82no—
969C2×C4—121no—
970C2×C4—121no—
971C2×C4—121no—
972C2×C4—128no—
973C2×C4—121no—
974C2×C4—122no—
975C2×C4—121no—
976C2×C4#95311yescharacteristic
977C2×C4#95311yescharacteristic
978C2×C4C2×D3×D411yescharacteristic
979C2×C4C2×#23711yescharacteristic
980C2×C4#100411yescharacteristic
981C2×C4#100411yescharacteristic
982C2×C4C22×#6711yescharacteristic
983C2×C4C22×#6711yescharacteristic
984C8—62no—
985C8—121no—
986C8—121no—
987C8—121no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—22no—
991C2×C3—41no—
992C2×C3—42no—
993C2×C3—81no—
994C2×C3—81no—
995C2×C3#241011yescharacteristic
996C2×C3C2×#45411yescharacteristic
997C2×C3#301811yescharacteristic
998D3—161no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—22no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—84no—
1018C22—242no—
1019C22—242no—
1020C22—241no—
1021C22—241no—
1022C22—241no—
1023C22#524512yescomplemented
1024C22D4×#6711yescharacteristic
1025C22#580611yescharacteristic
1026C22C2×#95311yescharacteristic
1027C4—21no—
1028C4—21no—
1029C4—22no—
1030C4—42no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—42no—
1035C4—41no—
1036C4—122no—
1037C4—122no—
1038C4—241no—
1039C4D4×#6711yescharacteristic
1040C4C2×#93911yescharacteristic
1041C4#580411yescharacteristic
1042C4#580611yescharacteristic
1043C3#2446511yescharacteristic, complemented, Sylow
1044C2—21no—
1045C2—22no—
1046C2—21no—
1047C2—41no—
1048C2—42no—
1049C2—81no—
1050C2—81no—
1051C2—481no—
1052C2#8404811yescharacteristic
1053C2C2×#524511yescharacteristic
1054C2#8412111yescharacteristic
subgroupG/H
centerC22C2×#953
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#3489C2
socleC22×C3C2×#120
hypercenter#3489D3
hypocenterC3#24465
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. C3×#3489C2semidirect
2. C2×#5245C2semidirect
3. #84082C2semidirect
4. C22×#837C2semidirect
5. #82924C2semidirect
6. #82809C2semidirect
7. #72143C2semidirect
8. #71879C2semidirect
9. #71877C2semidirect
10. #71867C2semidirect
11. #71863C2semidirect
12. #71711C2semidirect
13. #71698C2semidirect
14. #71667C2semidirect
15. #71665C2semidirect
36. C2×#949C22semidirect
37. C2×#947C22semidirect
49. C2×#837C22semidirect
50. C2×#837C22semidirect
53. #5232C22semidirect
54. #5229C22semidirect
56. C2×#836C22semidirect
57. C2×#836C22semidirect
64. #5001C22semidirect
65. #4995C22semidirect
67. #4988C22semidirect
68. #4977C22semidirect
70. #4532C22semidirect
71. #4532C22semidirect
72. #4530C22semidirect
73. #4530C22semidirect
74. #3489D3semidirect
205. #837D4semidirect
855. C22×C3#454semidirect
1023. C22#5245semidirect
1043. C3#24465semidirect

Maximal subgroups

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

subgroupindex
C3×#34892
C2×#52452
#840822
C22×#8372
#829242
#828092
#721432
#718792
#718772
#718672
#718632
#717112
#716982
#716672
#716652
#244653