Finite Group Databasebeta

← #25144087

Subgroups — #25144087

Order 11008.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583101C211yesmaximal, characteristic, complemented
2C2×#14583049C211yesmaximal, characteristic
3C2×#14583049C211yesmaximal, characteristic
4C2×C4×#10621884C211yesmaximal, characteristic, complemented
5C22⋊C4×D172C211yesmaximal, characteristic
6#19135966C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic, complemented
8#19135788C211yesmaximal, characteristic, complemented
9#19135678C211yesmaximal, characteristic, complemented
10#19135452C211yesmaximal, characteristic, complemented
11#19135203C211yesmaximal, characteristic, complemented
12#19134950C211yesmaximal, characteristic, complemented
13#19134932C211yesmaximal, characteristic, complemented
14#19134855C211yesmaximal, characteristic, complemented
15C43×#2429C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C22⋊C4×D43—21no—
24#14583101—24no—
25#14583049—24no—
26#14583049—24no—
27C4×#10621884—24no—
28C2×#13063256C2211yescharacteristic, complemented
29C2×#13063256C2211yescharacteristic, complemented
30C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
31C2×#13063249C2211yescharacteristic, complemented
32C2×#13063249C2211yescharacteristic, complemented
33C2×#13063249C2211yescharacteristic, complemented
34C2×#13063249C2211yescharacteristic, complemented
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic, complemented
42#14582801C2211yescharacteristic
43#14582801C2211yescharacteristic
44#14582777—21no—
45#14582777—21no—
46#14582759C2211yescharacteristic
47#14582754—21no—
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52C2×C4⋊Q8×C43C2211yescharacteristic, complemented
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic, complemented
56C43×#398—21no—
57C43×#396—21no—
58C43×#391C2211yescharacteristic, complemented
59C43×#389—21no—
60C43×#389C2211yescharacteristic, complemented
61C43×#388—21no—
62C4×C22⋊C4×C43C2211yescharacteristic
63C24×D43—21no—
64C22×D172—21no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—22no—
69C22×D172—41no—
70C22×D172—41no—
71C22×D172C2311yescharacteristic
72C22×D172C2311yescharacteristic
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C2×#10621884—22no—
76C2×#10621884—22no—
77C2×#10621884—22no—
78C2×#10621884—22no—
79C2×#10621884—22no—
80C2×#10621884—22no—
81C2×#10621884—22no—
82C2×#10621884—22no—
83C2×#10621884—22no—
84C2×#10621884—41no—
85C2×#10621884—41no—
86C2×#10621884D414yes—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C4×D172—22no—
92C4×D172—22no—
93C4×D172—41no—
94C4×D172—41no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C22⋊C4×D43—44no—
105#13063256—22no—
106#13063256—41no—
107C4⋊(C43⋊C8)—22no—
108#13063249—22no—
109#13063249—22no—
110#13063249—22no—
111#13063249—41no—
112#13063245—22no—
113#13063245—22no—
114#13063245—22no—
115#13063245D414yes—
116C22⋊(C43⋊C8)—22no—
117C22⋊(C43⋊C8)—22no—
118C4×C43⋊C8—22no—
119C43⋊#95—21no—
120C22×Q8×C43C2311yescharacteristic
121C22×Q8×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C4⋊Q8×C43—22no—
124C4⋊Q8×C43—41no—
125C22⋊Q8×C43—22no—
126C22⋊Q8×C43—22no—
127C22⋊Q8×C43—41no—
128C22⋊Q8×C43—41no—
129C4×Q8×C43—22no—
130C4×Q8×C43—41no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43D411yescharacteristic
142C2×C22⋊C4×C43D411yescharacteristic
143C2×C42×C43—21no—
144C2×C42×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43D411yescharacteristic
150#95×C43D411yescharacteristic
151C24×C43C2×D411yescharacteristic
152C23×D43—21no—
153C23×D43—21no—
154C23×D43—24no—
155C23×D43—42no—
156C23×D43—42no—
157C23×D43—42no—
158C23×D43—42no—
159C23×D43—81no—
160C23×D43—81no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43C2×D412yes—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C22×Dic43—21no—
190C22×Dic43—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—24no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—42no—
201C2×D172—42no—
202C2×D172—44no—
203C2×D172—44no—
204C2×D172—44no—
205C2×D172—44no—
206C2×D172C2×D412yes—
207C2×D172C2×D412yes—
208C2×D172#4112yes—
209C2×D172#4112yes—
210C2×C4×D43—42no—
211C2×C4×D43—42no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×C4×D43—81no—
215C2×C4×D43—81no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—42no—
220C4⋊C4×C43—42no—
221C4⋊C4×C43—42no—
222C4⋊C4×C43—42no—
223C4⋊C4×C43—42no—
224C4⋊C4×C43—42no—
225C4⋊C4×C43C2×D412yes—
226C22⋊C4×C43—41no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43SD1614yescomplemented
230C42×C43—21no—
231C42×C43—21no—
232C42×C43—21no—
233C42×C43—21no—
234C42×C43—42no—
235C22⋊Dic43—42no—
236#10621884—28no—
237#10621884—44no—
238#10621884—44no—
239#10621884—44no—
240(C2×D43)⋊C4—42no—
241(C2×D43)⋊C4—42no—
242(C2×D43)⋊C4—42no—
243(C2×D43)⋊C4—42no—
244(C2×D43)⋊C4—81no—
245(C2×D43)⋊C4—81no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8C2×D412yes—
261C2×C43⋊C8C2×D412yes—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43C2×SD1612yes—
269C23×C43C22×D411yescharacteristic
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—48no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—48no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—84no—
287C22×D43—84no—
288C22×D43—84no—
289C22×D43—84no—
290C22×D43—84no—
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—41no—
294Q8×C43—41no—
295Q8×C43—41no—
296Q8×C43—41no—
297Q8×C43—41no—
298Q8×C43—41no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43C2×SD1612yes—
329C2×C4×C43C2×SD1612yes—
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43C2×#4111yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342D172—22no—
343D172—22no—
344D172—22no—
345D172—22no—
346D172—22no—
347D172—48no—
348D172—41no—
349D172—41no—
350D172#12114yes—
351C4×D43—84no—
352C4×D43—84no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C43⋊C8—41no—
356C43⋊C8—41no—
357#25156—431nomaximal, Sylow
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43#52511yescharacteristic
366C22×C43D4211yescharacteristic
367C22×C43D4211yescharacteristic
368C22×C43C22×SD1611yescharacteristic
369C22×C43#57511yescharacteristic
370C22×C43#57711yescharacteristic
371C22×C43#57711yescharacteristic
372C2×D43—24no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—816no—
383C2×D43—81no—
384C2×D43—81no—
385C2×D43—81no—
386C2×D43—81no—
387C4×C43—22no—
388C4×C43—22no—
389C4×C43—41no—
390C4×C43—42no—
391C4×C43—41no—
392C4×C43—42no—
393C4×C43—41no—
394C4×C43—81no—
395C4×C43—81no—
396C4×C43C2×#12111yescharacteristic
397C4×C43#53811yescharacteristic
398C4×C43#54611yescharacteristic
399C4×C43#54611yescharacteristic
400Dic43—81no—
401Dic43—81no—
402C2×#461—431no—
403C2×#450—431no—
404C2×#450—431no—
405C2×C4×SD16—431no—
406#2429D4311yescharacteristic, complemented
407D4×C22⋊C4—431no—
408#2065—431no—
409#2035—431no—
410#2035—431no—
411#2013—431no—
412#1968—431no—
413#1923—431no—
414#1880—431no—
415#1877—431no—
416#1864—431no—
417C2×C43—42no—
418C2×C43#242411yescharacteristic
419C2×C43#310111yescharacteristic
420C2×C43#312311yescharacteristic
421C2×C43#326711yescharacteristic
422C2×C43#327511yescharacteristic
423C2×C43D4×SD1611yescharacteristic
424C2×C43D4×SD1611yescharacteristic
425D43—44no—
426D43—82no—
427C23×D4—431no—
428C22×SD16—431no—
429C22×SD16—431no—
430C22×SD16—431no—
431C22×SD16—431no—
432C2×C4⋊Q8C2×D4311yescharacteristic, complemented
433C2×C22⋊Q8C2×D4311yescharacteristic
434C2×C22⋊Q8C2×D4311yescharacteristic
435C2×C4×Q8C2×D4311yescharacteristic, complemented
436C2×C4×D4—431no—
437C2×C4×D4—431no—
438C22×C22⋊C4—861no—
439#461—864no—
440#450—864no—
441#450—864no—
442C4×SD16—864no—
443C2×#106—431no—
444C2×#106—431no—
445C2×C4⋊C8—431no—
446C2×#103—431no—
447C2×#103—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×C22⋊C8—431no—
455C2×C22⋊C8—431no—
456C2×C4×C8—431no—
457#398—21no—
458#396—21no—
459#391C2×D4311yescharacteristic, complemented
460#390—431no—
461#390—431no—
462#389—21no—
463#389C2×D4311yescharacteristic, complemented
464#388—21no—
465#386—861no—
466#386—861no—
467#380—431no—
468#379—861no—
469C4×C22⋊C4C2×D4311yescharacteristic
470#340—431no—
471#340—431no—
472#336—431no—
473#336—431no—
474C43#2515611yescharacteristic, complemented, Sylow
475C25—861no—
476C22×Q8C22×D4311yescharacteristic
477C22×Q8C22×D4311yescharacteristic
478C22×D4—431no—
479C22×D4—431no—
480C22×D4—862no—
481C22×D4—862no—
482C22×D4—862no—
483C22×D4—862no—
484C22×D4—861no—
485C22×D4—1721no—
486C22×D4—1721no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4C22×D4311yescharacteristic
490C2×SD16—434no—
491C2×SD16—862no—
492C2×SD16—862no—
493C2×SD16—862no—
494C2×SD16—862no—
495C2×SD16—862no—
496C2×SD16—862no—
497C2×SD16—862no—
498C2×SD16—862no—
499C2×SD16—862no—
500C2×SD16—1721no—
501C2×SD16—1721no—
502C22×C8—431no—
503C22×C8—431no—
504C22×C8—431no—
505C22×C8—431no—
506C4⋊Q8—22no—
507C4⋊Q8—41no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—41no—
511C22⋊Q8—41no—
512C4×Q8—22no—
513C4×Q8—41no—
514C4×D4—862no—
515C4×D4—862no—
516C4×D4—1721no—
517C4×D4—1721no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—431no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—1724no—
538C2×C22⋊C4C22⋊D4311yescharacteristic
539C2×C22⋊C4C22⋊D4311yescharacteristic
540C2×C42—21no—
541C2×C42C22×D4311yescharacteristic
542C2×C42C22×D4311yescharacteristic
543#106—862no—
544#106—1721no—
545C4⋊C8—862no—
546#103—862no—
547#103—862no—
548#103—862no—
549#103—1721no—
550#102—434no—
551#102—862no—
552#102—862no—
553#102—862no—
554C22⋊C8—862no—
555C22⋊C8—862no—
556C4×C8—862no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—861no—
561#95C22⋊D4311yescharacteristic
562#95C22⋊D4311yescharacteristic
563C24—864no—
564C24—861no—
565C24—861no—
566C24—3441no—
567C24—3441no—
568C24—1722no—
569C24—1722no—
570C24—1722no—
571C24—1722no—
572C24C2×C22⋊D4311yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8D4×D4312yes—
585C2×D4—432no—
586C2×D4—432no—
587C2×D4—432no—
588C2×D4—432no—
589C2×D4—864no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4—1722no—
599C2×D4—1722no—
600C2×D4—1724no—
601C2×D4—1724no—
602C2×D4—1724no—
603C2×D4—1724no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—3441no—
617C22×C4—3441no—
618C22×C4—1722no—
619C22×C4—1722no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4C2×C22⋊D4311yescharacteristic
623C22×C4C2×C22⋊D4311yescharacteristic
624C22×C4C2×C22⋊D4311yescharacteristic
625C22×C4C2×C22⋊D4311yescharacteristic
626C22×C4C2×C22⋊D4311yescharacteristic
627C22×C4C23×D4311yescharacteristic
628SD16—868no—
629SD16—1724no—
630SD16—1724no—
631SD16—1724no—
632C2×C8—432no—
633C2×C8—432no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4D4×D4312yes—
658C22⋊C4—41no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—3441no—
662C22⋊C4—3441no—
663C22⋊C4—1722no—
664C22⋊C4—1722no—
665C22⋊C4—1722no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4#1062188414yescomplemented
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—42no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—862no—
681C23—862no—
682C23—862no—
683C23—862no—
684C23—3444no—
685C23—3444no—
686C23—3444no—
687C23—3444no—
688C23—3444no—
689C23—1728no—
690C23—1728no—
691C23—1721no—
692C23—1721no—
693C23—1721no—
694C23—1721no—
695C23—1721no—
696C23—1721no—
697C23—1721no—
698C23—1721no—
699C23—1721no—
700C23—1721no—
701C23C2×#1062188412yes—
702C23C22×C22⋊D4311yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—434no—
712D4—862no—
713D4—862no—
714D4—862no—
715D4—862no—
716D4—862no—
717D4—1728no—
718D4—1721no—
719D4—1721no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—3444no—
750C2×C4—3444no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4C2×#1062188412yes—
758C2×C4C2×#1062188412yes—
759C2×C4C2×D4×D4311yescharacteristic
760C2×C4C2×D4×D4311yescharacteristic
761C2×C4#41×D4311yescharacteristic
762C2×C4#41×D4311yescharacteristic
763C2×C4#1306337011yescharacteristic
764C2×C4#1306337011yescharacteristic
765C8—862no—
766C8—862no—
767C8—1721no—
768C8—1721no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—864no—
777C22—34416no—
778C22—3441no—
779C22—3441no—
780C22—3441no—
781C22—3441no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22—1722no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22—1722no—
790C22—1722no—
791C22#1458340611yescharacteristic
792C22D4×C22⋊D4311yescharacteristic
793C22D4×C22⋊D4311yescharacteristic
794C22C22×#1062188411yescharacteristic
795C22#1458369711yescharacteristic
796C22#1458370711yescharacteristic
797C22#1458370711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—3441no—
808C4—3441no—
809C4#121×D4311yescharacteristic
810C4#1458348111yescharacteristic
811C4#1458353811yescharacteristic
812C4#1458354611yescharacteristic
813C2—42no—
814C2—3442no—
815C2—1724no—
816C2#1913812811yescharacteristic
817C2#1914459911yescharacteristic
818C2#1914484211yescharacteristic
819C2#1914612111yescharacteristic
820C2#1914622711yescharacteristic
821C2D4×#1062188411yescharacteristic
822C2D4×#1062188411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2429C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#2429D43
hypocenterC43#25156
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2429

Complements

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

NH ≅ G/Ntype
1. C2×#14583101C2semidirect
4. C2×C4×#10621884C2semidirect
6. #19135966C2semidirect
7. #19135788C2semidirect
8. #19135788C2semidirect
9. #19135678C2semidirect
10. #19135452C2semidirect
11. #19135203C2semidirect
12. #19134950C2semidirect
13. #19134932C2semidirect
14. #19134855C2semidirect
15. C43×#2429C2semidirect
28. C2×#13063256C22semidirect
29. C2×#13063256C22semidirect
30. C2×C4⋊(C43⋊C8)C22semidirect
31. C2×#13063249C22semidirect
32. C2×#13063249C22semidirect
33. C2×#13063249C22semidirect
34. C2×#13063249C22semidirect
41. C2×C4×C43⋊C8C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
52. C2×C4⋊Q8×C43C22semidirect
55. C2×C4×Q8×C43C22semidirect
58. C43×#391C22semidirect
60. C43×#389C22semidirect
229. C22⋊C4×C43SD16semidirect
406. #2429D43semidirect
432. C2×C4⋊Q8C2×D43semidirect
435. C2×C4×Q8C2×D43semidirect
459. #391C2×D43semidirect
463. #389C2×D43semidirect
474. C43#25156semidirect
668. C22⋊C4#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145831012
C2×#145830492
C2×C4×#106218842
C22⋊C4×D1722
#191359662
#191357882
#191356782
#191354522
#191352032
#191349502
#191349322
#191348552
C43×#24292
#2515643