Finite Group Databasebeta

← #25159516

Subgroups — #25159516

Order 11008.

896 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583200C211yesmaximal, characteristic, complemented
2C2×#14582941C211yesmaximal, characteristic, complemented
3#19138308C211yesmaximal, characteristic, complemented
4#19137609C211yesmaximal, characteristic
5#19136127C211yesmaximal, characteristic, complemented
6#19136093C211yesmaximal, characteristic, complemented
7#19135982C211yesmaximal, characteristic, complemented
8#19135934C211yesmaximal, characteristic, complemented
9#19135359C211yesmaximal, characteristic, complemented
10#19135167C211yesmaximal, characteristic, complemented
11#19135033C211yesmaximal, characteristic
12#19134915C211yesmaximal, characteristic
13#19134859C211yesmaximal, characteristic, complemented
14#19134790C211yesmaximal, characteristic, complemented
15C43×#1851C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×(C22⋊D43)⋊C4—21no—
20C2×#13063284C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22#14583200—24no—
23#14582941—24no—
24C2×#13063259C2211yescharacteristic
25C2×#13063259C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063257C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34#14582835—21no—
35#14582822—21no—
36#14582801C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582796—21no—
41#14582791—21no—
42#14582782—21no—
43#14582776—21no—
44#14582773—21no—
45#14582769C2211yescharacteristic
46#14582759C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C23×Dic43—21no—
64C22×C4×D43—21no—
65#13063317—22no—
66#13063317—41no—
67#13063299—22no—
68#13063299Q814yes—
69C4×D172—22no—
70C4×D172—41no—
71(C22⋊D43)⋊C4—44no—
72#13063284—22no—
73#13063284—41no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—41no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99#13063259—22no—
100#13063259D414yescomplemented
101#13063257—22no—
102#13063257—22no—
103#13063257—22no—
104#13063257—41no—
105#13063247—22no—
106#13063247—22no—
107#13063247—22no—
108#13063247—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C23×C4×C43C2311yescharacteristic
115C2×M16×C43—22no—
116C2×M16×C43—22no—
117C2×M16×C43—22no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C22⋊C4×C43D411yescharacteristic
123C2×C22⋊C4×C43D411yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C4⋊C8×C43—22no—
127C4⋊C8×C43—22no—
128C22⋊C8×C43—22no—
129#95×C43D411yescharacteristic
130#95×C43D411yescharacteristic
131C24×C43C2×D411yescharacteristic
132C23×D43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×Q812yes—
143C22×C4×C43#4112yes—
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—24no—
146C2×C22⋊D43—42no—
147C2×C22⋊D43—42no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43—81no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172C2×Q812yes—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—81no—
167M16×C43—28no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
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×C43C2×D412yes—
179C2×C8×C43#4112yes—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—41no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C22⋊Dic43—42no—
187C22⋊Dic43—81no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—42no—
204C4⋊Dic43—42no—
205C4⋊Dic43—81no—
206C4⋊Dic43C2×D412yes—
207C4⋊Dic43C2×D412yes—
208C4⋊Dic43C2×Q812yes—
209Dic43⋊C4—42no—
210Dic43⋊C4—42no—
211Dic43⋊C4—42no—
212Dic43⋊C4—42no—
213Dic43⋊C4—81no—
214C4×Dic43—42no—
215C4×Dic43—42no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43C22⋊Q812yes—
223C23×C43C22×D411yescharacteristic
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
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×C43C22⋊Q812yes—
249C2×C4×C43AGL(1,ℤ/8)12yes—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×Q811yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C22⋊D43—48no—
257C2×Dic43—22no—
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—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—84no—
279D172—22no—
280D172—22no—
281D172—41no—
282D172—41no—
283C4×D43—84no—
284C8×C43—22no—
285C8×C43—22no—
286C8×C43—41no—
287C8×C43—41no—
288#26366—431nomaximal, Sylow
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43C2×C22⋊Q811yescharacteristic
297C22×C43D4211yescharacteristic
298C22×C43#54711yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43#57511yescharacteristic
301C22×C43#57711yescharacteristic
302C22×C43#57711yescharacteristic
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C4×C43—22no—
311C4×C43—22no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43#52511yescharacteristic
316C4×C43#53911yescharacteristic
317C4×C43D4×Q811yescharacteristic
318C4×C43#55411yescharacteristic
319Dic43—42no—
320Dic43—42no—
321Dic43—42no—
322Dic43—81no—
323Dic43—81no—
324Dic43—81no—
325Dic43—81no—
326C2×#478—431no—
327C2×#428—431no—
328#2441—431no—
329#2361—431no—
330#2094—431no—
331#2088—431no—
332#2067—431no—
333#2059—431no—
334#1948—431no—
335#1918—431no—
336#1895—431no—
337#1875—431no—
338#1864—431no—
339#1853—431no—
340#1851D4311yescharacteristic, complemented
341C2×C43—42no—
342C2×C43#244911yescharacteristic
343C2×C43#307711yescharacteristic
344C2×C43#308411yescharacteristic
345C2×C43#327111yescharacteristic
346C2×C43#327211yescharacteristic
347C2×C43#334511yescharacteristic
348C2×C43#335111yescharacteristic
349D43—82no—
350C22×M16C2×D4311yescharacteristic
351C2×#125—431no—
352C2×#121—431no—
353C2×C4×D4—431no—
354C2×C4×D4—861no—
355C2×#117—431no—
356C22×C4⋊C4—431no—
357#478—864no—
358#428—864no—
359C2×#107—431no—
360C2×#107—431no—
361C2×#106—431no—
362C2×#106—431no—
363C2×#106—431no—
364C2×#106—431no—
365C2×C4⋊C8C2×D4311yescharacteristic
366C2×C4⋊C8C2×D4311yescharacteristic
367C2×#102—431no—
368C2×#102—431no—
369C2×#102—431no—
370C2×#102—431no—
371C2×C22⋊C8C2×D4311yescharacteristic
372#399—861no—
373#396—861no—
374#390—431no—
375#389—431no—
376#389—431no—
377#389—431no—
378#389—861no—
379#388—861no—
380#387—861no—
381#386—861no—
382#385—861no—
383#384—431no—
384#380—431no—
385C4×C4⋊C4—431no—
386C4×C22⋊C4C2×D4311yescharacteristic
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#336C2×D4311yescharacteristic
394#336C2×D4311yescharacteristic
395C43#2636611yescharacteristic, complemented, Sylow
396C22×D4—431no—
397C22×D4—861no—
398C23×C4—861no—
399C23×C4—861no—
400C23×C4C22×D4311yescharacteristic
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—22no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408#125—862no—
409#125—1721no—
410#121—434no—
411#121—862no—
412C4×D4—862no—
413C4×D4—1721no—
414C4×D4—1724no—
415#117—862no—
416#117—1721no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—1721no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4D17211yescharacteristic
441C2×C22⋊C4D17211yescharacteristic
442C2×C42—861no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445C2×C42C22×D4311yescharacteristic
446#107—434no—
447#107—862no—
448#106—862no—
449#106—862no—
450#106—862no—
451#106—1721no—
452C4⋊C8—22no—
453C4⋊C8—22no—
454#102—862no—
455#102—862no—
456#102—862no—
457#102—1721no—
458C22⋊C8—22no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95D17211yescharacteristic
465#95D17211yescharacteristic
466C24—861no—
467C24C2×D17211yescharacteristic
468C2×D4—432no—
469C2×D4—864no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—1722no—
476C2×D4—1722no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—3441no—
489C22×C4—3441no—
490C22×C4—1722no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4C2×D17211yescharacteristic
495C22×C4C2×D17211yescharacteristic
496C22×C4C2×D17211yescharacteristic
497C22×C4C2×D17211yescharacteristic
498C22×C4C2×D17211yescharacteristic
499C22×C4#1062190012yes—
500C22×C4Q8×D4312yes—
501C22×C4C23×D4311yescharacteristic
502M16—28no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8D4×D4312yes—
514C2×C8#1062190012yes—
515C4⋊C4—432no—
516C4⋊C4—432no—
517C4⋊C4—432no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—3441no—
530C4⋊C4—3441no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C22⋊C4—22no—
538C22⋊C4—41no—
539C22⋊C4—864no—
540C22⋊C4—3441no—
541C22⋊C4—3441no—
542C22⋊C4—1722no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—1722no—
550C42—1722no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—862no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23#1306330512yes—
565C23C22×D17211yescharacteristic
566D4—862no—
567D4—862no—
568D4—1728no—
569D4—1721no—
570D4—1721no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—3444no—
592C2×C4—3444no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
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#1306330512yes—
612C2×C4#1306335312yes—
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4C2×Q8×D4311yescharacteristic
615C2×C4C2×#1062190011yescharacteristic
616C2×C4C2×#1062190011yescharacteristic
617C2×C4#1306337111yescharacteristic
618C2×C4#1306337211yescharacteristic
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—3441no—
631C22—3441no—
632C22—3441no—
633C22—3441no—
634C22—1722no—
635C22—1722no—
636C22—1722no—
637C22C2×#1306330511yescharacteristic
638C22D4×D17211yescharacteristic
639C22#1458355311yescharacteristic
640C22C2×#1306335311yescharacteristic
641C22#1458369911yescharacteristic
642C22#1458371111yescharacteristic
643C22#1458371111yescharacteristic
644C4—22no—
645C4—22no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—3441no—
650C4—3441no—
651C4—3441no—
652C4—3441no—
653C4—1722no—
654C4—1722no—
655C4—1722no—
656C4#1458340511yescharacteristic
657C4#1458349311yescharacteristic
658C4#1458356211yescharacteristic
659C4#1458360711yescharacteristic
660C2—42no—
661C2—3442no—
662C2#1913840211yescharacteristic
663C2#1914439411yescharacteristic
664C2#1914445911yescharacteristic
665C2#1914618511yescharacteristic
666C2#1914619711yescharacteristic
667C2#1914706711yescharacteristic
668C2#1914715711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1851C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1851D43
hypocenterC43#26366
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#14583200C2semidirect
2. C2×#14582941C2semidirect
3. #19138308C2semidirect
5. #19136127C2semidirect
6. #19136093C2semidirect
7. #19135982C2semidirect
8. #19135934C2semidirect
9. #19135359C2semidirect
10. #19135167C2semidirect
13. #19134859C2semidirect
14. #19134790C2semidirect
15. C43×#1851C2semidirect
100. #13063259D4semidirect
340. #1851D43semidirect
395. C43#26366semidirect

Maximal subgroups

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

subgroupindex
C2×#145832002
C2×#145829412
#191383082
#191376092
#191361272
#191360932
#191359822
#191359342
#191353592
#191351672
#191350332
#191349152
#191348592
#191347902
C43×#18512
#2636643