Finite Group Databasebeta

← #25159763

Subgroups — #25159763

Order 11008.

932 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583200C211yesmaximal, characteristic, complemented
2C2×C4×D344C211yesmaximal, characteristic
3#19138467C211yesmaximal, characteristic, complemented
4C4⋊C4×D172C211yesmaximal, characteristic, complemented
5#19136127C211yesmaximal, characteristic, complemented
6#19136068C211yesmaximal, characteristic, complemented
7#19135968C211yesmaximal, characteristic, complemented
8#19135934C211yesmaximal, characteristic, complemented
9#19135323C211yesmaximal, characteristic, complemented
10#19134942C211yesmaximal, characteristic
11#19134942C211yesmaximal, characteristic
12#19134859C211yesmaximal, characteristic, complemented
13#19134859C211yesmaximal, characteristic, complemented
14#19134845C211yesmaximal, characteristic, complemented
15C43×#1916C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4⋊C4×D43—21no—
23#14583200—24no—
24C4×D344—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063259C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063257C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36#14582834—21no—
37#14582823—21no—
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582797C2211yescharacteristic
44#14582773—21no—
45#14582773—21no—
46#14582770—21no—
47#14582769C2211yescharacteristic
48#14582758—21no—
49#14582756—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C2×D344—22no—
68C2×D344—22no—
69C2×D344Q814yes—
70#13063317—22no—
71#13063317—41no—
72C4×D172—22no—
73C4×D172—22no—
74C4×D172—22no—
75C4×D172—22no—
76C4×D172—22no—
77C4×D172—41no—
78C4×D172—41no—
79C4×D172—41no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C4⋊C4×D43—44no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—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—
103#13063259—22no—
104#13063259—22no—
105#13063257—22no—
106#13063257—22no—
107#13063257—41no—
108#13063247—22no—
109#13063247—22no—
110#13063247—22no—
111#13063247—22no—
112#13063247—41no—
113#13063247D414yes—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C4⋊C8×C43—22no—
128C4×C8×C43—22no—
129#95×C43D411yescharacteristic
130#95×C43D411yescharacteristic
131C23×D43—21no—
132C23×D43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C2×D412yes—
155C2×D172C2×Q812yes—
156C2×D172C2×Q812yes—
157C2×D172#4112yes—
158C2×C4×D43—24no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—81no—
168C2×C4×D43—81no—
169C2×C4×D43—81no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43C2×D412yes—
181C2×C8×C43C2×Q812yes—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—81no—
196(C2×D43)⋊C4—81no—
197(C2×D43)⋊C4—81no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—42no—
209C4⋊Dic43—81no—
210C4⋊Dic43C2×D412yes—
211C4⋊Dic43#4112yes—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4—42no—
215Dic43⋊C4—42no—
216Dic43⋊C4—81no—
217Dic43⋊C4—81no—
218D344—28no—
219C23×C43C22×D411yescharacteristic
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43#13512yes—
251C2×C4×C43AGL(1,ℤ/8)12yes—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×Q811yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276D172—22no—
277D172—22no—
278D172—22no—
279D172—22no—
280D172—22no—
281D172—41no—
282D172—41no—
283D172C22⋊Q814yes—
284C4×D43—48no—
285C4×D43—84no—
286C4×D43—84no—
287C4×D43—84no—
288C8×C43—22no—
289C8×C43—22no—
290C8×C43—41no—
291C8×C43—41no—
292#26382—431nomaximal, Sylow
293C22×C43#52511yescharacteristic
294C22×C43D4211yescharacteristic
295C22×C43D4×Q811yescharacteristic
296C22×C43C2×#13511yescharacteristic
297C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C43#57611yescharacteristic
299C22×C43#57711yescharacteristic
300C2×D43—24no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—41no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43C2×C22⋊Q811yescharacteristic
321C4×C43#53911yescharacteristic
322C4×C43#54711yescharacteristic
323C4×C43#55411yescharacteristic
324Dic43—42no—
325Dic43—42no—
326Dic43—81no—
327Dic43—81no—
328Dic43—81no—
329Dic43—81no—
330C2×#478—431no—
331C2×C4×D8—431no—
332#2454—431no—
333D4×C4⋊C4—431no—
334#2094—431no—
335#2083—431no—
336#2065—431no—
337#2059—431no—
338#1941—431no—
339#1916D4311yescharacteristic, complemented
340#1879—431no—
341#1879—431no—
342#1864—431no—
343#1864—431no—
344#1862—431no—
345C2×C43#244911yescharacteristic
346C2×C43#310511yescharacteristic
347C2×C43#311911yescharacteristic
348C2×C43#326411yescharacteristic
349C2×C43#328411yescharacteristic
350C2×C43#338011yescharacteristic
351C2×C43#338411yescharacteristic
352D43—44no—
353D43—82no—
354C22×D8—431no—
355C2×#125—431no—
356C2×C4×D4—431no—
357C2×C4×D4—431no—
358C2×C4×D4—431no—
359C2×C4×D4—431no—
360C22×C4⋊C4—861no—
361#478—864no—
362C4×D8—864no—
363C2×#107—431no—
364C2×#107—431no—
365C2×#106—431no—
366C2×#106—431no—
367C2×#106—431no—
368C2×C4⋊C8C2×D4311yescharacteristic
369C2×#102—431no—
370C2×#102—431no—
371C2×#102—431no—
372C2×#102—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×C4×C8C2×D4311yescharacteristic
376#399—861no—
377#396—861no—
378#390—431no—
379#390—431no—
380#389—431no—
381#389—431no—
382#389—431no—
383#389—431no—
384#385—861no—
385#385—861no—
386#385—861no—
387#384—431no—
388#380—861no—
389#380—861no—
390C4×C4⋊C4C2×D4311yescharacteristic
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#336C2×D4311yescharacteristic
396#336C2×D4311yescharacteristic
397#336C2×D4311yescharacteristic
398#336C2×D4311yescharacteristic
399C43#2638211yescharacteristic, complemented, Sylow
400C22×D4—431no—
401C22×D4—431no—
402C23×C4—861no—
403C23×C4—861no—
404C23×C4—861no—
405C23×C4—861no—
406C2×D8—434no—
407C2×D8—862no—
408C2×D8—862no—
409C22×C8C22×D4311yescharacteristic
410C22×C8C22×D4311yescharacteristic
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413#125—862no—
414#125—1721no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—1721no—
421C4×D4—1721no—
422C4×D4—1721no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—1724no—
438C2×C4⋊C4D17211yescharacteristic
439C2×C4⋊C4D17211yescharacteristic
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C42C22×D4311yescharacteristic
449C2×C42C22×D4311yescharacteristic
450C2×C42C22×D4311yescharacteristic
451#107—862no—
452#107—862no—
453#106—862no—
454#106—862no—
455#106—1721no—
456C4⋊C8—22no—
457#102—434no—
458#102—862no—
459#102—862no—
460#102—862no—
461#102—862no—
462#102—1721no—
463C4×C8—22no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95D17211yescharacteristic
469#95D17211yescharacteristic
470C24—861no—
471C24—861no—
472C2×D4—432no—
473C2×D4—432no—
474C2×D4—432no—
475C2×D4—432no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C22×C4—864no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—3441no—
492C22×C4—3441no—
493C22×C4—3441no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4—1722no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4—1722no—
501C22×C4—1722no—
502C22×C4C2×D17211yescharacteristic
503C22×C4C2×D17211yescharacteristic
504C22×C4C2×D17211yescharacteristic
505C22×C4C2×D17211yescharacteristic
506C22×C4C2×D17211yescharacteristic
507C22×C4C2×D17211yescharacteristic
508C22×C4C23×D4311yescharacteristic
509D8—868no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8D4×D4312yes—
521C2×C8Q8×D4312yes—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—432no—
525C4⋊C4—432no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—3441no—
537C4⋊C4—3441no—
538C4⋊C4—3441no—
539C4⋊C4—1722no—
540C4⋊C4—1722no—
541C4⋊C4—1722no—
542C4⋊C4—1722no—
543C4⋊C4—1722no—
544C22⋊C4—864no—
545C22⋊C4—3441no—
546C22⋊C4—3441no—
547C22⋊C4—3441no—
548C22⋊C4—1722no—
549C22⋊C4—1722no—
550C22⋊C4—1722no—
551C22⋊C4—1722no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C23—862no—
559C23—862no—
560C23—862no—
561C23—862no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23C22×D17211yescharacteristic
573D4—434no—
574D4—862no—
575D4—862no—
576D4—862no—
577D4—862no—
578D4—862no—
579D4—1721no—
580D4—1721no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—3444no—
600C2×C4—3444no—
601C2×C4—3444no—
602C2×C4—1728no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4#1306334712yes—
620C2×C4#1306335312yes—
621C2×C4C2×D4×D4311yescharacteristic
622C2×C4C2×Q8×D4311yescharacteristic
623C2×C4#41×D4311yescharacteristic
624C2×C4#41×D4311yescharacteristic
625C2×C4#1306337111yescharacteristic
626C2×C4#1306337211yescharacteristic
627C8—22no—
628C8—22no—
629C8—41no—
630C8—41no—
631C22—864no—
632C22—3441no—
633C22—3441no—
634C22—3441no—
635C22—3441no—
636C22—1722no—
637C22—1722no—
638C22—1722no—
639C22—1722no—
640C22—1722no—
641C22—1722no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22#1458341111yescharacteristic
646C22D4×D17211yescharacteristic
647C22Q8×D17211yescharacteristic
648C22C2×#1306334711yescharacteristic
649C22C2×#1306335311yescharacteristic
650C22#1458370411yescharacteristic
651C22#1458371111yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—3441no—
659C4—3441no—
660C4—3441no—
661C4—3441no—
662C4—1722no—
663C4—1722no—
664C4C22⋊Q8×D4311yescharacteristic
665C4#1458349011yescharacteristic
666C4#1458354711yescharacteristic
667C4#1458360511yescharacteristic
668C2—3442no—
669C2—1724no—
670C2#1913840911yescharacteristic
671C2#1914464411yescharacteristic
672C2#1914479611yescharacteristic
673C2#1914608011yescharacteristic
674C2#1914632711yescharacteristic
675C2#1914746311yescharacteristic
676C2#1914749611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1916C2
socleC23×C43C22×D4
prime radicalC22×D344C22
hypercenter#1916D43
hypocenterC43#26382
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. C2×#14583200C2semidirect
3. #19138467C2semidirect
4. C4⋊C4×D172C2semidirect
5. #19136127C2semidirect
6. #19136068C2semidirect
7. #19135968C2semidirect
8. #19135934C2semidirect
9. #19135323C2semidirect
12. #19134859C2semidirect
13. #19134859C2semidirect
14. #19134845C2semidirect
15. C43×#1916C2semidirect
339. #1916D43semidirect
399. C43#26382semidirect

Maximal subgroups

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

subgroupindex
C2×#145832002
C2×C4×D3442
#191384672
C4⋊C4×D1722
#191361272
#191360682
#191359682
#191359342
#191353232
#191349422
#191348592
#191348452
C43×#19162
#2638243