Finite Group Databasebeta

← #10828186

Subgroups — #10828186

Order 768.

1462 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5806C211yesmaximal, characteristic
2C2×#4772C211yesmaximal, characteristic, complemented
3C2×#4779C211yesmaximal, characteristic, complemented
4#74025C211yesmaximal, characteristic, complemented
5C3×#1786C211yesmaximal, characteristic, complemented
6#72128C211yesmaximal, characteristic, complemented
7#70216C211yesmaximal, characteristic, complemented
8#70202C211yesmaximal, characteristic, complemented
9#70199C211yesmaximal, characteristic, complemented
10#70178C211yesmaximal, characteristic, complemented
11#70170C211yesmaximal, characteristic, complemented
12#70167C211yesmaximal, characteristic, complemented
13#69957C211yesmaximal, characteristic, complemented
14#69936C211yesmaximal, characteristic, complemented
15#69527C211yesmaximal, characteristic, complemented
16#24037—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×#237C2211yescharacteristic
19C2×#953—21no—
20C22×#217—21no—
21#5806—24no—
22#5806—24no—
23C2×#939—21no—
24C2×#938C2211yescharacteristic
25C2×#936C2211yescharacteristic
26C2×#935—21no—
27C2×D4×Dic3C2211yescharacteristic
28C2×C4×#67C2211yescharacteristic
29C2×#924C2211yescharacteristic
30C22×D3×C8C2211yescharacteristic, complemented
31C2×#892C2211yescharacteristic, complemented
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5212C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
45C2×#817C2211yescharacteristic, complemented
46C2×#816C2211yescharacteristic, complemented
47C2×#816C2211yescharacteristic, complemented
48#4987C2211yescharacteristic, complemented
49#4984C2211yescharacteristic, complemented
50#4972C2211yescharacteristic, complemented
51C2×#810C2211yescharacteristic, complemented
52C2×#810C2211yescharacteristic, complemented
53C2×#807C2211yescharacteristic, complemented
54#4961—21no—
55#4945—21no—
56#4779—24no—
57#4772—24no—
58#4675—21no—
59#4654—21no—
60#4551C2211yescharacteristic, complemented
61#4550C2211yescharacteristic, complemented
62#4550C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64C2×#546—31no—
65C2×#482—31no—
66C2×#416—31no—
67#2485—31no—
68#2042—31no—
69#2042—31no—
70#2036—31no—
71#2035—31no—
72#1893—31no—
73#1869—31no—
74#1864—31no—
75#1862—31no—
76#1788—31no—
77#1786—31no—
78#1786D311yescharacteristic, complemented
79C25×C3—21no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—21no—
85C22×C3×D4—41no—
86C22×C3×D4—41no—
87C22×C3×D4C2311yescharacteristic
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C22×#67—21no—
91C22×#67—21no—
92C22×#67D411yescharacteristic
93C23×Dic3—21no—
94C23×Dic3—21no—
95C2×#237—22no—
96C2×#237—22no—
97C2×#237—22no—
98C2×#237—41no—
99C2×#237—41no—
100C2×#237D414yes—
101C22×C4×D3C2311yescharacteristic
102C22×Dic6C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108#953—28no—
109C2×#217—28no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217D411yescharacteristic
117#939—28no—
118#938—22no—
119#938D414yes—
120#936—22no—
121#936—22no—
122#935—28no—
123D4×Dic3—22no—
124D4×Dic3—22no—
125C4×#67—22no—
126C4×#67—22no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4D411yescharacteristic
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134#924—22no—
135#924—22no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4D411yescharacteristic
139C2×C4×Dic3—21no—
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×D3×C8—22no—
144C2×D3×C8—41no—
145C2×D3×C8—41no—
146#892—22no—
147#892—22no—
148C3×#102—22no—
149C3×#102—22no—
150C3×#102—22no—
151C3×#102—41no—
152C3×C22⋊C8—41no—
153C3×#95—21no—
154#832—22no—
155#832—22no—
156#832—22no—
157#832—41no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#830—41no—
163(C2×D3)⋊C8—22no—
164#817—22no—
165#816—22no—
166#816—41no—
167#810—22no—
168#810—41no—
169#807—22no—
170C22×#41—31no—
171C23×D4C2×D311yescharacteristic
172C23×C8—31no—
173#546—64no—
174#546—64no—
175C2×#124—31no—
176C2×#123—61no—
177C2×C22⋊Q8—31no—
178C2×#121—31no—
179C2×#121—61no—
180C2×#120—61no—
181C2×C4×D4—31no—
182C2×C4×D4—31no—
183C2×#117—31no—
184C22×C22⋊C4—61no—
185#482—64no—
186C2×#107—31no—
187C2×#106—31no—
188#416—64no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102C2×D311yescharacteristic
198C2×#102C2×D311yescharacteristic
199C2×#102C2×D311yescharacteristic
200C2×#102C2×D311yescharacteristic
201C2×C22⋊C8—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8C2×D311yescharacteristic
204#397—61no—
205#394—61no—
206#389—31no—
207#389—31no—
208#388—61no—
209#387—61no—
210#380—31no—
211#380—31no—
212#380C2×D311yescharacteristic
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3—24no—
219C24×C3—21no—
220C24×C3—42no—
221C24×C3—42no—
222C24×C3—42no—
223C24×C3—42no—
224C24×C3—81no—
225C24×C3—81no—
226C24×C3C2×D411yescharacteristic
227C23×D3C2×D411yescharacteristic
228C2×C3×D4—24no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—44no—
240C2×C3×D4—44no—
241C2×C3×D4—44no—
242C2×C3×D4—44no—
243C2×C3×D4C2×D412yes—
244C2×C3×D4C2×D412yes—
245C2×C3×D4#4112yes—
246C2×C3×D4#4112yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2411yescharacteristic
257C2×#67—22no—
258C2×#67—22no—
259C2×#67—24no—
260C2×#67—24no—
261C2×#67—41no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—81no—
265C2×#67—81no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—24no—
269C22×Dic3—24no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—42no—
273C22×Dic3—42no—
274C22×Dic3—81no—
275C22×Dic3—81no—
276C22×Dic3C2×D411yescharacteristic
277C22×Dic3C2×D411yescharacteristic
278C22×Dic3C2×D411yescharacteristic
279#237—28no—
280#237—44no—
281#237—44no—
282#237—44no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3C2×D412yes—
288C2×C4×D3C2×D412yes—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6C2×D412yes—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C22⋊C4—81no—
306#217—24no—
307#217—24no—
308#217—24no—
309#217—24no—
310#217—22no—
311#217—24no—
312#217—42no—
313(C2×D3)⋊C4—22no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—81no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—42no—
322C4⋊Dic3C2×D412yes—
323Dic3⋊C4—24no—
324Dic3⋊C4—22no—
325Dic3⋊C4—81no—
326C4×Dic3—21no—
327C4×Dic3—21no—
328C4×Dic3—42no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335D3×C8—44no—
336C25—21no—
337C2×#41—34no—
338C2×#41—62no—
339C2×#41—62no—
340C2×#41—62no—
341C2×#41—121no—
342C2×#41—121no—
343C22×Q8—31no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—21no—
349C22×D4—31no—
350C22×D4—41no—
351C22×D4—41no—
352C22×D4—61no—
353C22×D4—61no—
354C22×D4C22×D311yescharacteristic
355C22×D4C22×D311yescharacteristic
356C23×C4—31no—
357C23×C4—61no—
358C23×C4—61no—
359C23×C4C22×D311yescharacteristic
360C22×C8—31no—
361C22×C8—31no—
362C22×C8—62no—
363C22×C8—121no—
364C22×C8—121no—
365C22×C8C22×D311yescharacteristic
366C22×C8C22×D311yescharacteristic
367#124—62no—
368#124—62no—
369#123—68no—
370C22⋊Q8—62no—
371C22⋊Q8—62no—
372#121—34no—
373#121—62no—
374#121—68no—
375#120—68no—
376C4×D4—62no—
377C4×D4—62no—
378C4×D4—62no—
379C4×D4—62no—
380#117—62no—
381#117—62no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—31no—
393C2×C22⋊C4—31no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—68no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C42—31no—
404C2×C42—61no—
405#107—62no—
406#106—62no—
407#103—62no—
408#103—62no—
409#103—121no—
410#103—121no—
411#102—22no—
412#102—22no—
413#102—22no—
414#102—41no—
415#102—62no—
416#102—62no—
417#102—62no—
418#102—121no—
419C22⋊C8—41no—
420C22⋊C8—62no—
421C22⋊C8—121no—
422#95—21no—
423#95—61no—
424#95—61no—
425#95—61no—
426#95—61no—
427C23×C3—21no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—48no—
438C23×C3—48no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—84no—
450C23×C3—84no—
451C23×C3—84no—
452C23×C3—84no—
453C23×C3—84no—
454C23×C3#13512yes—
455C23×C3C22×D411yescharacteristic
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3#12012yes—
463C3×D4—22no—
464C3×D4—22no—
465C3×D4—22no—
466C3×D4—22no—
467C3×D4—22no—
468C3×D4—48no—
469C3×D4—41no—
470C3×D4—41no—
471C3×D4#12314yes—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
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×C4C22×D411yescharacteristic
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4C2×#4111yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×C3×C4H(5,𝔽2)11yescharacteristic
490C2×C3×C4H(5,𝔽2)11yescharacteristic
491#67—48no—
492#67—44no—
493#67—84no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—48no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—84no—
516C2×Dic3#12012yes—
517C4×D3—22no—
518C4×D3—22no—
519C4×D3—22no—
520C4×D3—22no—
521Dic6—22no—
522Dic6—22no—
523Dic6—41no—
524Dic6—41no—
525C3×C8—41no—
526C3×C8—41no—
527C3⋊C8—41no—
528C3⋊C8—41no—
529C24—21no—
530C24—24no—
531C24—21no—
532C24—31no—
533C24—42no—
534C24—42no—
535C24—42no—
536C24—42no—
537C24—81no—
538C24—81no—
539C24D3×D411yescharacteristic
540#41—68no—
541#41—124no—
542#41—124no—
543#41—124no—
544C2×Q8—32no—
545C2×Q8—61no—
546C2×Q8—61no—
547C2×Q8—61no—
548C2×Q8—61no—
549C2×Q8—61no—
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—62no—
566C2×D4—64no—
567C2×D4—62no—
568C2×D4—64no—
569C2×D4—121no—
570C2×D4—122no—
571C2×D4—122no—
572C2×D4—241no—
573C2×D4—241no—
574C2×D4#23512yes—
575C2×D4D3×D412yes—
576C2×D4D3×D412yes—
577C2×D4#23712yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—31no—
587C22×C4—32no—
588C22×C4—32no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—64no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—64no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—122no—
602C22×C4—122no—
603C22×C4—241no—
604C22×C4—241no—
605C22×C4D3×D411yescharacteristic
606C22×C4C23×D311yescharacteristic
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—
619C2×C8—124no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—32no—
625C4⋊C4—62no—
626C4⋊C4—64no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—122no—
633C4⋊C4—241no—
634C22⋊C4—62no—
635C22⋊C4—62no—
636C22⋊C4—64no—
637C22⋊C4—64no—
638C22⋊C4—64no—
639C22⋊C4—64no—
640C22⋊C4—64no—
641C22⋊C4—81no—
642C22⋊C4—122no—
643C22⋊C4—122no—
644C22⋊C4—241no—
645C42—61no—
646C42—61no—
647C42—122no—
648C22×C3—24no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—41no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—41no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—41no—
659C22×C3—42no—
660C22×C3—41no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—816no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3C2×#12011yescharacteristic
671C22×C3#54611yescharacteristic
672C22×C3#54611yescharacteristic
673C22×C3C2×#13511yescharacteristic
674C22×C3#57511yescharacteristic
675C22×C3#57611yescharacteristic
676C22×C3#57711yescharacteristic
677C2×D3—22no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C3×C4—41no—
685C3×C4—81no—
686C3×C4—81no—
687C3×C4C2×#12311yescharacteristic
688C3×C4#53411yescharacteristic
689C3×C4#54611yescharacteristic
690C3×C4#54611yescharacteristic
691Dic3—22no—
692Dic3—42no—
693Dic3—41no—
694Dic3—41no—
695Dic3—42no—
696Dic3—81no—
697Dic3—81no—
698C23—21no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—32no—
709C23—48no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—61no—
722C23—61no—
723C23—61no—
724C23—61no—
725C23—61no—
726C23—61no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23#91612yes—
733C23C2×D3×D411yescharacteristic
734Q8—62no—
735Q8—62no—
736Q8—121no—
737Q8—121no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—48no—
744D4—41no—
745D4—41no—
746D4—124no—
747D4—128no—
748D4—244no—
749D4#88314yes—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—32no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—128no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—244no—
790C2×C4C2×#23511yescharacteristic
791C2×C4C2×D3×D411yescharacteristic
792C2×C4C2×D3×D411yescharacteristic
793C2×C4C2×#23711yescharacteristic
794C2×C4#100411yescharacteristic
795C2×C4#100411yescharacteristic
796C8—41no—
797C8—41no—
798C8—121no—
799C8—121no—
800C2×C3—42no—
801C2×C3—44no—
802C2×C3—82no—
803C2×C3#240511yescharacteristic
804C2×C3#300211yescharacteristic
805C2×C3#301211yescharacteristic
806C2×C3#329611yescharacteristic
807C2×C3#329711yescharacteristic
808C2×C3#331111yescharacteristic
809C2×C3#331911yescharacteristic
810D3—42no—
811C22—22no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—62no—
829C22—62no—
830C22—62no—
831C22—816no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22#549011yescharacteristic
841C22D3×#12011yescharacteristic
842C22#559111yescharacteristic
843C22#575711yescharacteristic
844C22C2×#91611yescharacteristic
845C22#577311yescharacteristic
846C22#577511yescharacteristic
847C4—41no—
848C4—62no—
849C4—81no—
850C4—81no—
851C4—121no—
852C4—122no—
853C4—121no—
854C4—122no—
855C4—241no—
856C4—241no—
857C4C2×#88311yescharacteristic
858C4#549011yescharacteristic
859C4#558911yescharacteristic
860C4#559111yescharacteristic
861C3#2403711yescharacteristic, complemented, Sylow
862C2—42no—
863C2—44no—
864C2—82no—
865C2—122no—
866C2#7385311yescharacteristic
867C2#7876011yescharacteristic
868C2#7893511yescharacteristic
869C2#8000511yescharacteristic
870C2#8001911yescharacteristic
871C2#8014511yescharacteristic
872C2#8015911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1786C2
socleC23×C3C22×D4
prime radicalC2×#5806C2
hypercenter#1786D3
hypocenterC3#24037
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#4772C2semidirect
3. C2×#4779C2semidirect
4. #74025C2semidirect
5. C3×#1786C2semidirect
6. #72128C2semidirect
7. #70216C2semidirect
8. #70202C2semidirect
9. #70199C2semidirect
10. #70178C2semidirect
11. #70170C2semidirect
12. #70167C2semidirect
13. #69957C2semidirect
14. #69936C2semidirect
15. #69527C2semidirect
30. C22×D3×C8C22semidirect
31. C2×#892C22semidirect
44. C2×(C2×D3)⋊C8C22semidirect
45. C2×#817C22semidirect
46. C2×#816C22semidirect
47. C2×#816C22semidirect
48. #4987C22semidirect
49. #4984C22semidirect
50. #4972C22semidirect
51. C2×#810C22semidirect
52. C2×#810C22semidirect
53. C2×#807C22semidirect
60. #4551C22semidirect
61. #4550C22semidirect
62. #4550C22semidirect
63. #4529C22semidirect
78. #1786D3semidirect
861. C3#24037semidirect

Maximal subgroups

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

subgroupindex
C2×#58062
C2×#47722
C2×#47792
#740252
C3×#17862
#721282
#702162
#702022
#701992
#701782
#701702
#701672
#699572
#699362
#695272
#240373