Finite Group Databasebeta

← #10944089

Subgroups — #10944089

Order 768.

1506 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5574C211yesmaximal, characteristic, complemented
2C2×#5172C211yesmaximal, characteristic, complemented
3C2×#5163C211yesmaximal, characteristic, complemented
4C2×#4810C211yesmaximal, characteristic, complemented
5C2×#4786C211yesmaximal, characteristic, complemented
6#76456C211yesmaximal, characteristic, complemented
7C3×#1880C211yesmaximal, characteristic, complemented
8#71633C211yesmaximal, characteristic, complemented
9#70222C211yesmaximal, characteristic, complemented
10#70200C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#68893C211yesmaximal, characteristic, complemented
13#68880C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68663C211yesmaximal, characteristic, complemented
16#32913—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#940C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C22×D24C2211yescharacteristic
26#5574—24no—
27#5574—24no—
28C2×#895C2211yescharacteristic
29C2×#893—21no—
30C2×#893C2211yescharacteristic
31C2×D3×C4⋊C4—21no—
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×C4×D12—21no—
34C2×C4×D12C2211yescharacteristic
35C2×#872—21no—
36C2×#872C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5172—24no—
43#5163—24no—
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49C2×Dic3⋊C8C2211yescharacteristic
50#4977C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53#4960—21no—
54#4960—21no—
55#4959—21no—
56#4959—21no—
57#4939C2211yescharacteristic
58#4810—24no—
59#4786—24no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65#4524C2211yescharacteristic
66C2×#520—31no—
67C2×#460—31no—
68C2×#459—31no—
69C2×#449—31no—
70C2×#449—31no—
71#2619—31no—
72#1880—31no—
73#1880D311yescharacteristic, complemented
74#1879—31no—
75#1879—31no—
76#1874—31no—
77#1874—31no—
78#1805—31no—
79#1804—31no—
80#1798—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—22no—
91C2×#239D414yescomplemented
92C22×D12—21no—
93C22×D12—21no—
94C22×D12C2311yescharacteristic
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3—21no—
100C22×C4×D3C2311yescharacteristic
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×C4×Q8—22no—
107C3×C4×Q8—22no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C42—21no—
114C2×C3×C42C2311yescharacteristic
115C2×#217—21no—
116Q8×Dic3—22no—
117Q8×Dic3D414yescomplemented
118C2×#215—22no—
119C2×#215—22no—
120C2×#215—22no—
121#940—22no—
122#940—22no—
123#938—22no—
124#938—22no—
125C2×#213—22no—
126C2×#213—22no—
127C2×#213—22no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4D411yescharacteristic
134C2×(C2×D3)⋊C4D411yescharacteristic
135C2×C4⋊Dic3—21no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4D411yescharacteristic
140C2×Dic3⋊C4D411yescharacteristic
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D24—22no—
146C2×D24—22no—
147C2×D24—22no—
148#895—22no—
149#895—22no—
150#893—28no—
151#893—22no—
152#893D414yescomplemented
153D3×C4⋊C4—28no—
154D3×C4⋊C4—22no—
155D3×C4⋊C4—22no—
156C4×D12—28no—
157C4×D12—22no—
158C4×D12—22no—
159#872—28no—
160#872—22no—
161#872—22no—
162C3×#103—22no—
163C3×#102—22no—
164#835—22no—
165#832—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168#821—22no—
169#821—22no—
170(C2×D3)⋊C8—22no—
171(C2×D3)⋊C8—22no—
172Dic3⋊C8—22no—
173Dic3⋊C8—22no—
174#809—22no—
175#809—22no—
176C22×#41—31no—
177C22×SD16—31no—
178C22×SD16C2×D311yescharacteristic
179C22×D8—31no—
180C22×D8—31no—
181C2×#127—31no—
182C2×#121—31no—
183C2×#121—31no—
184#520—64no—
185#520—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8C2×D311yescharacteristic
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×#117—31no—
193C2×#117—61no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—61no—
196#460—64no—
197#459—64no—
198#449—64no—
199#449—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103C2×D311yescharacteristic
204C2×#102—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212#394—61no—
213#394—61no—
214#392—61no—
215#392—61no—
216#390—31no—
217#390C2×D311yescharacteristic
218#382—31no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340C2×D311yescharacteristic
223#336—31no—
224#336C2×D311yescharacteristic
225C24×C3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3C2×D411yescharacteristic
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8C2×D412yes—
233C2×C3×Q8C2×D412yes—
234C2×C3×Q8#4112yes—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—81no—
251C2×#67—81no—
252C2×#67—81no—
253C2×#67—81no—
254C2×#67—81no—
255C2×#67—81no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261#239—28no—
262#239—28no—
263#239—28no—
264#239—28no—
265C2×D12—24no—
266C2×D12—24no—
267C2×D12—24no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—42no—
278C2×D12—81no—
279C2×D12—81no—
280C2×D12C2×D412yes—
281C2×D12C2×D412yes—
282C2×D12#4112yes—
283C2×C4×D3—24no—
284C2×C4×D3—24no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—24no—
290C2×C4×D3—24no—
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×D3—81no—
298C2×C4×D3—81no—
299C2×C4×D3C2×D412yes—
300C2×C4×D3#4112yes—
301C3×SD16—44no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4C2×D412yes—
313C3×C22⋊C4—81no—
314C3×C22⋊C4—81no—
315C3×C42—24no—
316C3×C42—21no—
317C3×C42—21no—
318#217—42no—
319#215—44no—
320#213—44no—
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—
326(C2×D3)⋊C4—81no—
327(C2×D3)⋊C4—81no—
328C4⋊Dic3—21no—
329C4⋊Dic3—24no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3C2×D412yes—
333Dic3⋊C4—24no—
334Dic3⋊C4—22no—
335Dic3⋊C4—22no—
336C4×Dic3—24no—
337C4×Dic3C2×D412yes—
338C4×Dic3C2×D412yes—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345D24—44no—
346C2×#41—34no—
347C2×#41—62no—
348C2×#41—62no—
349C2×#41—62no—
350C2×#41—62no—
351C2×#41—62no—
352C22×Q8C22×D311yescharacteristic
353C22×D4—31no—
354C22×D4—31no—
355C22×D4—61no—
356C22×D4—61no—
357C22×D4—61no—
358C22×D4—61no—
359C22×D4—61no—
360C22×D4C22×D311yescharacteristic
361C23×C4—31no—
362C23×C4—61no—
363C23×C4—61no—
364C23×C4—61no—
365C23×C4—61no—
366C2×SD16—22no—
367C2×SD16—22no—
368C2×SD16—22no—
369C2×SD16—62no—
370C2×SD16—62no—
371C2×SD16—62no—
372C2×D8—62no—
373C2×D8—62no—
374C2×D8—62no—
375C2×D8—62no—
376C2×D8—62no—
377C2×D8—62no—
378C22×C8—31no—
379C22×C8—31no—
380C22×C8C22×D311yescharacteristic
381C22×C8C22×D311yescharacteristic
382#127—62no—
383#127—62no—
384#121—62no—
385#121—62no—
386#121—62no—
387#121—62no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—34no—
391C4×Q8—62no—
392C4×D4—34no—
393C4×D4—62no—
394C4×D4—62no—
395C4×D4—68no—
396C4×D4—62no—
397C4×D4—68no—
398#117—62no—
399#117—62no—
400#117—68no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—62no—
407C2×C4⋊C4—68no—
408C2×C4⋊C4—61no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—31no—
416C2×C22⋊C4—31no—
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×C42—21no—
424C2×C42—31no—
425C2×C42—61no—
426C2×C42C22×D311yescharacteristic
427C4⋊C8—62no—
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—41no—
442C23×C3—41no—
443C23×C3—41no—
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—41no—
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#12112yes—
470C3×Q8—22no—
471C3×Q8—22no—
472C3×Q8—22no—
473C3×Q8#12114yes—
474C3×D4—41no—
475C3×D4—41no—
476C3×D4—41no—
477C3×D4—41no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499#67—84no—
500#67—84no—
501#67—84no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3#12012yes—
515C2×Dic3#12012yes—
516C2×Dic3#12112yes—
517D12—216no—
518D12—22no—
519D12—22no—
520D12—22no—
521D12—41no—
522D12—41no—
523D12—41no—
524D12—41no—
525D12—84no—
526D12#12114yes—
527C4×D3—216no—
528C4×D3—22no—
529C4×D3—22no—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—84no—
533C4×D3—84no—
534C4×D3—84no—
535C3×C8—41no—
536C3×C8—41no—
537C3⋊C8—41no—
538C3⋊C8—41no—
539C24—21no—
540C24—31no—
541C24—61no—
542C24—61no—
543#41—68no—
544#41—68no—
545#41—68no—
546#41—68no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8#23512yes—
551C2×Q8D3×D412yes—
552C2×Q8D3×D412yes—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—32no—
560C2×D4—32no—
561C2×D4—32no—
562C2×D4—64no—
563C2×D4—64no—
564C2×D4—64no—
565C2×D4—61no—
566C2×D4—61no—
567C2×D4—61no—
568C2×D4—61no—
569C2×D4—61no—
570C2×D4—61no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—122no—
575C2×D4—122no—
576C2×D4—122no—
577C2×D4—122no—
578C2×D4—241no—
579C2×D4—241no—
580C2×D4—241no—
581C2×D4—241no—
582C2×D4—241no—
583C2×D4—241no—
584C2×D4—241no—
585C2×D4—241no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—64no—
595C22×C4—64no—
596C22×C4—64no—
597C22×C4—64no—
598C22×C4—64no—
599C22×C4—64no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—241no—
607C22×C4—241no—
608C22×C4—241no—
609C22×C4—241no—
610C22×C4—241no—
611C22×C4—241no—
612C22×C4D3×D411yescharacteristic
613C22×C4D3×D411yescharacteristic
614C22×C4C23×D311yescharacteristic
615SD16—44no—
616SD16—124no—
617D8—124no—
618D8—124no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—61no—
626C2×C8—61no—
627C2×C8—61no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—32no—
636C4⋊C4—62no—
637C4⋊C4—62no—
638C4⋊C4—64no—
639C4⋊C4—64no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4D3×D412yes—
644C22⋊C4—62no—
645C22⋊C4—62no—
646C22⋊C4—64no—
647C22⋊C4—64no—
648C22⋊C4—81no—
649C22⋊C4—81no—
650C22⋊C4—122no—
651C22⋊C4—122no—
652C22⋊C4—241no—
653C22⋊C4—241no—
654C42—24no—
655C42—21no—
656C42—21no—
657C42—32no—
658C42—32no—
659C42—64no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3C2×#12011yescharacteristic
668C22×C3C2×#12111yescharacteristic
669C22×C3#52511yescharacteristic
670C22×C3#57611yescharacteristic
671C22×C3#57611yescharacteristic
672C22×C3#57711yescharacteristic
673C22×C3#57711yescharacteristic
674C2×D3—22no—
675C2×D3—24no—
676C2×D3—22no—
677C2×D3—22no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—42no—
681C2×D3—42no—
682C2×D3—41no—
683C2×D3—42no—
684C2×D3—41no—
685C2×D3—42no—
686C2×D3—42no—
687C2×D3—42no—
688C2×D3—81no—
689C2×D3—81no—
690C2×D3—81no—
691C2×D3—81no—
692C2×D3—81no—
693C2×D3—81no—
694C2×D3—81no—
695C3×C4—24no—
696C3×C4—41no—
697C3×C4—42no—
698C3×C4—41no—
699C3×C4—81no—
700C3×C4C2×#12111yescharacteristic
701C3×C4C2×#12111yescharacteristic
702C3×C4#52511yescharacteristic
703C3×C4#52511yescharacteristic
704Dic3—22no—
705Dic3—22no—
706Dic3—22no—
707Dic3—42no—
708Dic3—81no—
709C23—32no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—61no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23—62no—
722C23—61no—
723C23—62no—
724C23—61no—
725C23—62no—
726C23—121no—
727C23—121no—
728C23—121no—
729C23—121no—
730C23—121no—
731C23—121no—
732C23—121no—
733C23—121no—
734C23—121no—
735C23—121no—
736C23—121no—
737C23C2×D3×D411yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8#88414yes—
742D4—34no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—616no—
748D4—62no—
749D4—62no—
750D4—62no—
751D4—121no—
752D4—121no—
753D4—121no—
754D4—121no—
755D4—244no—
756D4—244no—
757D4—244no—
758D4—244no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—616no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—244no—
795C2×C4—244no—
796C2×C4—244no—
797C2×C4C2×#23511yescharacteristic
798C2×C4C2×D3×D411yescharacteristic
799C2×C4C2×D3×D411yescharacteristic
800C2×C4C2×D3×D411yescharacteristic
801C2×C4D3×#4111yescharacteristic
802C2×C4D3×#4111yescharacteristic
803C8—41no—
804C8—41no—
805C8—121no—
806C8—121no—
807C2×C3—161no—
808C2×C3#284711yescharacteristic
809C2×C3#300811yescharacteristic
810C2×C3#301011yescharacteristic
811C2×C3#304511yescharacteristic
812C2×C3#304511yescharacteristic
813C2×C3#311911yescharacteristic
814C2×C3#311911yescharacteristic
815D3—42no—
816D3—44no—
817D3—161no—
818C22—62no—
819C22—64no—
820C22—62no—
821C22—62no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—122no—
830C22—121no—
831C22—122no—
832C22—121no—
833C22—122no—
834C22—121no—
835C22—122no—
836C22—121no—
837C22—122no—
838C22—122no—
839C22—241no—
840C22—241no—
841C22—241no—
842C22—241no—
843C22—241no—
844C22—241no—
845C22—241no—
846C22#554711yescharacteristic
847C22D3×#12011yescharacteristic
848C22D3×#12111yescharacteristic
849C22#576211yescharacteristic
850C22#576911yescharacteristic
851C22#577411yescharacteristic
852C22#577811yescharacteristic
853C4—24no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—62no—
858C4—62no—
859C4—62no—
860C4—81no—
861C4—122no—
862C4—241no—
863C4C2×#88411yescharacteristic
864C4#554711yescharacteristic
865C4D3×#12111yescharacteristic
866C4#565611yescharacteristic
867C3#3291311yescharacteristic, complemented, Sylow
868C2—122no—
869C2—124no—
870C2—161no—
871C2—481no—
872C2#7493511yescharacteristic
873C2#7969711yescharacteristic
874C2#7981211yescharacteristic
875C2#8004111yescharacteristic
876C2#8008511yescharacteristic
877C2#8038611yescharacteristic
878C2#8060211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1880C2
socleC23×C3C22×D4
hypercenter#1880D3
hypocenterC3#32913
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×#5574C2semidirect
2. C2×#5172C2semidirect
3. C2×#5163C2semidirect
4. C2×#4810C2semidirect
5. C2×#4786C2semidirect
6. #76456C2semidirect
7. C3×#1880C2semidirect
8. #71633C2semidirect
9. #70222C2semidirect
10. #70200C2semidirect
11. #69657C2semidirect
12. #68893C2semidirect
13. #68880C2semidirect
14. #68673C2semidirect
15. #68663C2semidirect
73. #1880D3semidirect
91. C2×#239D4semidirect
117. Q8×Dic3D4semidirect
152. #893D4semidirect
867. C3#32913semidirect

Maximal subgroups

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

subgroupindex
C2×#55742
C2×#51722
C2×#51632
C2×#48102
C2×#47862
#764562
C3×#18802
#716332
#702222
#702002
#696572
#688932
#688802
#686732
#686632
#329133