Finite Group Databasebeta

← #25156645

Subgroups — #25156645

Order 11008.

918 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic43C211yesmaximal, characteristic, complemented
2#19138356C211yesmaximal, characteristic
3Q8×Dic43⋊C4C211yesmaximal, characteristic, complemented
4#19136126C211yesmaximal, characteristic, complemented
5#19136093C211yesmaximal, characteristic, complemented
6#19136001C211yesmaximal, characteristic, complemented
7#19135826C211yesmaximal, characteristic
8#19135275C211yesmaximal, characteristic, complemented
9#19135149C211yesmaximal, characteristic, complemented
10#19134952C211yesmaximal, characteristic, complemented
11#19134952C211yesmaximal, characteristic, complemented
12#19134952C211yesmaximal, characteristic, complemented
13#19134863C211yesmaximal, characteristic, complemented
14#19134854C211yesmaximal, characteristic, complemented
15C2×C43×#460C211yesmaximal, characteristic
16C2×#13063306—21no—
17C2×Q8×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20SD16×Dic43—24no—
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582813—21no—
31#14582813—21no—
32#14582802C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582797—21no—
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582795—21no—
39#14582795C2211yescharacteristic
40#14582779—21no—
41#14582768—21no—
42#14582768C2211yescharacteristic
43C4×Dic43⋊C4—21no—
44C4×Dic43⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×#127×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C43×#460—24no—
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C23×Dic43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063306—44no—
65Q8×Dic43—22no—
66Q8×Dic43—22no—
67Q8×Dic43—22no—
68Q8×Dic43—41no—
69D4×Dic43—22no—
70D4×Dic43—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4D411yescharacteristic
83C2×Dic43⋊C4D411yescharacteristic
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063257—22no—
96#13063256—41no—
97#13063249—22no—
98#13063249—22no—
99#13063246—22no—
100#13063246—22no—
101#13063246—22no—
102#13063246—41no—
103C8×Dic43—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43—21no—
111C22×D4×C43—21no—
112C22×D4×C43C2311yescharacteristic
113C22×D4×C43C2311yescharacteristic
114C2×SD16×C43—22no—
115C2×SD16×C43—22no—
116C2×SD16×C43—22no—
117C2×SD16×C43—22no—
118C2×SD16×C43—22no—
119C2×SD16×C43D414yes—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122#127×C43—22no—
123#127×C43—41no—
124C4×Q8×C43—22no—
125C4×Q8×C43—41no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—22no—
131#102×C43—22no—
132#102×C43—22no—
133C24×C43—21no—
134C24×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43C2×D412yes—
139C2×Q8×C43#4112yes—
140C2×Q8×C43#4112yes—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43—42no—
155C2×D4×C43—42no—
156C2×D4×C43—81no—
157C2×D4×C43—81no—
158C2×D4×C43C2×D412yes—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—42no—
169C22×Dic43—42no—
170C22×Dic43—81no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175SD16×C43—28no—
176SD16×C43—44no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43C2×D412yes—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—42no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—42no—
192C22⋊Dic43—42no—
193C22⋊Dic43—81no—
194C22⋊Dic43—81no—
195C22⋊Dic43—81no—
196C4⋊Dic43—24no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—42no—
205C4⋊Dic43#4112yes—
206Dic43⋊C4—41no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—81no—
210Dic43⋊C4—81no—
211Dic43⋊C4—81no—
212Dic43⋊C4SD1614yescomplemented
213C4×Dic43—24no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—42no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C23×C43—22no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43C22×D411yescharacteristic
240Q8×C43—22no—
241Q8×C43—22no—
242Q8×C43—22no—
243Q8×C43#12314yescomplemented
244D4×C43—22no—
245D4×C43—22no—
246D4×C43—41no—
247D4×C43—41no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—41no—
252D4×C43—84no—
253D4×C43—84no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—21no—
257C2×C4×C43—22no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43C2×SD1612yes—
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43H(5,𝔽2)11yescharacteristic
271C2×C4×C432−1+411yescharacteristic
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—22no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—84no—
295C2×Dic43C2×SD1612yes—
296C2×Dic43C2×SD1612yes—
297C8×C43—22no—
298C8×C43—41no—
299C43⋊C8—41no—
300C43⋊C8—41no—
301#26163—431nomaximal, Sylow
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43—81no—
316C22×C43#52511yescharacteristic
317C22×C43D4211yescharacteristic
318C22×C43#54811yescharacteristic
319C22×C43C22×SD1611yescharacteristic
320C22×C43#57511yescharacteristic
321C22×C43#57611yescharacteristic
322C22×C43#57711yescharacteristic
323C4×C43—24no—
324C4×C43—22no—
325C4×C43—41no—
326C4×C43—81no—
327C4×C43C2×#12311yescharacteristic
328C4×C43#53911yescharacteristic
329C4×C43#54711yescharacteristic
330C4×C43#55311yescharacteristic
331Dic43—22no—
332Dic43—22no—
333Dic43—41no—
334Dic43—42no—
335Dic43—41no—
336Dic43—81no—
337Dic43—81no—
338Dic43—81no—
339C2×#460D4311yescharacteristic
340C2×C4×SD16—431no—
341#2445—431no—
342Q8×C4⋊C4—431no—
343#2094—431no—
344#2088—431no—
345#2071—431no—
346#2041—431no—
347#1934—431no—
348#1916—431no—
349#1880—431no—
350#1880—431no—
351#1880—431no—
352#1865—431no—
353#1864—431no—
354C2×C43—82no—
355C2×C43—161no—
356C2×C43#244311yescharacteristic
357C2×C43#310311yescharacteristic
358C2×C43#311911yescharacteristic
359C2×C43#326811yescharacteristic
360C2×C43D4×SD1611yescharacteristic
361C2×C43#336211yescharacteristic
362C2×C43#337111yescharacteristic
363C22×SD16C2×D4311yescharacteristic
364C22×SD16C2×D4311yescharacteristic
365C2×#127C2×D4311yescharacteristic
366C2×#123—861no—
367C2×C4×Q8—431no—
368C2×C4×Q8—431no—
369C2×C4×Q8C2×D4311yescharacteristic
370C2×C4×D4—431no—
371#460—24no—
372C4×SD16—864no—
373C2×#106—431no—
374C2×#106—431no—
375C2×C4⋊C8C2×D4311yescharacteristic
376C2×#103—431no—
377C2×#103—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#102C2×D4311yescharacteristic
383C2×#102C2×D4311yescharacteristic
384C2×C4×C8—431no—
385#394—861no—
386#394—861no—
387#390—431no—
388#390—431no—
389#390—431no—
390#389—431no—
391#389—431no—
392#389—431no—
393#389—861no—
394#389—861no—
395#386—861no—
396#384—431no—
397#384—861no—
398C4×C4⋊C4—431no—
399C4×C4⋊C4—861no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#336—431no—
405#336—431no—
406#336—431no—
407#336—431no—
408C43#2616311yescharacteristic, complemented, Sylow
409C22×Q8C22×D4311yescharacteristic
410C22×D4—21no—
411C22×D4—21no—
412C22×D4C22×D4311yescharacteristic
413C22×D4C22×D4311yescharacteristic
414C23×C4—861no—
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—22no—
418C2×SD16—22no—
419C2×SD16—22no—
420C2×SD16C22⋊D4314yes—
421C22×C8—431no—
422C22×C8—431no—
423C22×C8C22×D4311yescharacteristic
424C22×C8C22×D4311yescharacteristic
425#127—22no—
426#127—41no—
427#123—1724no—
428C4×Q8—22no—
429C4×Q8—41no—
430C4×Q8—862no—
431C4×Q8—862no—
432C4×Q8—862no—
433C4×Q8—1721no—
434C4×D4—862no—
435C4×D4—1721no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C42—21no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42C22×D4311yescharacteristic
464#106—862no—
465#106—1721no—
466C4⋊C8—22no—
467#103—862no—
468#103—862no—
469#102—22no—
470#102—22no—
471#102—862no—
472#102—862no—
473#102—862no—
474#102—1721no—
475C4×C8—862no—
476#95—431no—
477#95—431no—
478#95—861no—
479#95—861no—
480#95—861no—
481C24—21no—
482C24—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8#1062190012yes—
487C2×Q8#1062190012yes—
488C2×Q8C2×C22⋊D4312yes—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4C2×C22⋊D4312yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—3441no—
518C22×C4—1722no—
519C22×C4—1722no—
520C22×C4D4×D4311yescharacteristic
521C22×C4D4×D4311yescharacteristic
522C22×C4C23×D4311yescharacteristic
523SD16—28no—
524SD16—44no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8C2×C22⋊D4312yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—434no—
541C4⋊C4—432no—
542C4⋊C4—864no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—3441no—
551C4⋊C4—3441no—
552C4⋊C4—3441no—
553C4⋊C4—1721no—
554C4⋊C4—1722no—
555C4⋊C4—1722no—
556C4⋊C4—1722no—
557C22⋊C4—3441no—
558C22⋊C4—3441no—
559C22⋊C4—3441no—
560C22⋊C4—1722no—
561C22⋊C4—1722no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—864no—
568C42—861no—
569C42—861no—
570C42—861no—
571C42—861no—
572C42—1722no—
573C23—22no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23C2×D4×D4311yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—22no—
591Q8#1306330614yescomplemented
592D4—22no—
593D4—22no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—84no—
601D4—84no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—432no—
614C2×C4—432no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—862no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—3444no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4SD16×D4312yes—
639C2×C4C22×C22⋊D4311yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4C2×#1062190011yescharacteristic
642C2×C4C2×#1062190011yescharacteristic
643C2×C4#1306337011yescharacteristic
644C2×C4#1306337211yescharacteristic
645C8—22no—
646C8—41no—
647C8—1721no—
648C8—1721no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22#1458340911yescharacteristic
664C22D4×C22⋊D4311yescharacteristic
665C22#1458355511yescharacteristic
666C22C2×SD16×D4311yescharacteristic
667C22#1458369511yescharacteristic
668C22#1458370311yescharacteristic
669C22#1458370511yescharacteristic
670C4—24no—
671C4—22no—
672C4—41no—
673C4—81no—
674C4—862no—
675C4—862no—
676C4—3441no—
677C4—3441no—
678C4—3441no—
679C4—1721no—
680C4—1722no—
681C4—1721no—
682C4C2×#1306330611yescharacteristic
683C4#1458349411yescharacteristic
684C4#1458354811yescharacteristic
685C4#1458359211yescharacteristic
686C2—82no—
687C2—161no—
688C2#1913832611yescharacteristic
689C2#1914462511yescharacteristic
690C2#1914479311yescharacteristic
691C2#1914612911yescharacteristic
692C2SD16×C22⋊D4311yescharacteristic
693C2#1914726111yescharacteristic
694C2#1914735611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#460C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
hypercenterC2×#460D43
hypocenterC43#26163
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic43C2semidirect
3. Q8×Dic43⋊C4C2semidirect
4. #19136126C2semidirect
5. #19136093C2semidirect
6. #19136001C2semidirect
8. #19135275C2semidirect
9. #19135149C2semidirect
10. #19134952C2semidirect
11. #19134952C2semidirect
12. #19134952C2semidirect
13. #19134863C2semidirect
14. #19134854C2semidirect
212. Dic43⋊C4SD16semidirect
243. Q8×C43#123semidirect
408. C43#26163semidirect
591. Q8#13063306semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic432
#191383562
Q8×Dic43⋊C42
#191361262
#191360932
#191360012
#191358262
#191352752
#191351492
#191349522
#191348632
#191348542
C2×C43×#4602
#2616343