Finite Group Databasebeta

← #25159524

Subgroups — #25159524

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×#14583197C211yesmaximal, characteristic, complemented
2C2×#14582941C211yesmaximal, characteristic, complemented
3#19138309C211yesmaximal, characteristic, complemented
4#19137615C211yesmaximal, characteristic
5#19136126C211yesmaximal, characteristic, complemented
6#19136095C211yesmaximal, characteristic, complemented
7#19135981C211yesmaximal, characteristic, complemented
8#19135936C211yesmaximal, characteristic, complemented
9#19135357C211yesmaximal, characteristic, complemented
10#19135165C211yesmaximal, characteristic, complemented
11#19134918C211yesmaximal, characteristic
12#19134858C211yesmaximal, characteristic, complemented
13#19134787C211yesmaximal, characteristic, complemented
14#19134778C211yesmaximal, characteristic, complemented
15C43×#1895C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×D4×Dic43—21no—
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21#14583197—24no—
22#14582941—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063259C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582835—21no—
35#14582822—21no—
36#14582802C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582796—21no—
40#14582795C2211yescharacteristic
41#14582792—21no—
42#14582786—21no—
43#14582779—21no—
44#14582774—21no—
45#14582768C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47C4×C22⋊Dic43C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C2×#121×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063316—22no—
66#13063316—41no—
67D4×Dic43—22no—
68D4×Dic43—41no—
69D4×Dic43—44no—
70#13063284—22no—
71#13063284—41no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—41no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43D411yescharacteristic
91C2×C22⋊Dic43D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063259—22no—
97#13063259D414yescomplemented
98#13063257—22no—
99#13063257—22no—
100#13063256—22no—
101#13063256—41no—
102Dic43⋊C8—22no—
103Dic43⋊C8—22no—
104#13063246—22no—
105#13063246—41no—
106C22⋊(C43⋊C8)—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C22×D4×C43—21no—
114C22×D4×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C2×M16×C43—22no—
117C2×M16×C43—22no—
118C2×M16×C43—22no—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121#121×C43—22no—
122#121×C43Q814yes—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128#102×C43—22no—
129#102×C43—22no—
130#95×C43—21no—
131C24×C43—21no—
132C24×C43C2×D411yescharacteristic
133C2×D4×C43—21no—
134C2×D4×C43—24no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—42no—
140C2×D4×C43—42no—
141C2×D4×C43C2×Q812yes—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×Q812yes—
151C22×C4×C43#4112yes—
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43—81no—
162C22×Dic43—81no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167M16×C43—28no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D412yes—
173C2×C8×C43#4112yes—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×Q812yes—
180C22⋊C4×C43—24no—
181C22⋊C4×C43—81no—
182C22⋊Dic43—22no—
183C22⋊Dic43—41no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187C22⋊Dic43—81no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—42no—
195C4⋊Dic43—42no—
196C4⋊Dic43—42no—
197C4⋊Dic43—81no—
198C4⋊Dic43C2×D412yes—
199C4⋊Dic43C2×D412yes—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202Dic43⋊C4—42no—
203Dic43⋊C4—81no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—42no—
209C4×Dic43—42no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—22no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43C22⋊Q812yes—
230C23×C43C22×D411yescharacteristic
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—48no—
234D4×C43—41no—
235D4×C43—41no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43C22⋊Q812yes—
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—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—84no—
282C2×Dic43—84no—
283C2×Dic43AGL(1,ℤ/8)12yes—
284C8×C43—22no—
285C8×C43—22no—
286C43⋊C8—41no—
287C43⋊C8—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×C43—42no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43C2×C22⋊Q811yescharacteristic
304C22×C43D4211yescharacteristic
305C22×C43#54711yescharacteristic
306C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C43#57511yescharacteristic
308C22×C43#57711yescharacteristic
309C22×C43#57711yescharacteristic
310C4×C43—22no—
311C4×C43—42no—
312C4×C43—81no—
313C4×C43—81no—
314C4×C43#52511yescharacteristic
315C4×C43#53911yescharacteristic
316C4×C43D4×Q811yescharacteristic
317C4×C43#55411yescharacteristic
318Dic43—22no—
319Dic43—41no—
320Dic43—41no—
321Dic43—41no—
322Dic43—42no—
323Dic43—42no—
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#1895D4311yescharacteristic
337#1875—431no—
338#1864—431no—
339#1853—431no—
340#1851—431no—
341C2×C43—42no—
342C2×C43—82no—
343C2×C43#244911yescharacteristic
344C2×C43#307711yescharacteristic
345C2×C43#308411yescharacteristic
346C2×C43#327111yescharacteristic
347C2×C43#327211yescharacteristic
348C2×C43#334511yescharacteristic
349C2×C43#335111yescharacteristic
350C22×M16C2×D4311yescharacteristic
351C2×#125—431no—
352C2×#121C2×D4311yescharacteristic
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⋊C8—431no—
366C2×C4⋊C8—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×#102C2×D4311yescharacteristic
370C2×#102C2×D4311yescharacteristic
371C2×C22⋊C8—431no—
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#380C2×D4311yescharacteristic
385C4×C4⋊C4—431no—
386C4×C22⋊C4—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340C2×D4311yescharacteristic
392#340C2×D4311yescharacteristic
393#336—431no—
394#336—431no—
395C43#2636611yescharacteristic, complemented, Sylow
396C22×D4—21no—
397C22×D4C22×D4311yescharacteristic
398C23×C4—861no—
399C23×C4—861no—
400C23×C4C22×D4311yescharacteristic
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—22no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408#125—862no—
409#125—1721no—
410#121—22no—
411#121Dic8614yes—
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—862no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—1721no—
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—431no—
437C2×C22⋊C4—431no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446#107—434no—
447#107—862no—
448#106—862no—
449#106—862no—
450#106—862no—
451#106—1721no—
452C4⋊C8—862no—
453C4⋊C8—862no—
454#102—22no—
455#102—22no—
456#102—862no—
457#102—1721no—
458C22⋊C8—862no—
459#95—21no—
460#95—431no—
461#95—431no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466C24—21no—
467C24D4×D4311yescharacteristic
468C2×D4—24no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4C2×Dic8612yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—3441no—
493C22×C4—3441no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4—1722no—
498C22×C4C2×Dic8612yes—
499C22×C4D4×D4311yescharacteristic
500C22×C4#1062190012yes—
501C22×C4C23×D4311yescharacteristic
502M16—28no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8D4×D4312yes—
514C2×C8#1062190012yes—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—432no—
521C4⋊C4—432no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—3441no—
529C4⋊C4—3441no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4C2×Dic8612yes—
537C22⋊C4—24no—
538C22⋊C4—81no—
539C22⋊C4—862no—
540C22⋊C4—3441no—
541C22⋊C4—1722no—
542C22⋊C4—1721no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42—861no—
549C42—1722no—
550C42—1722no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—22no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23#1306330212yes—
565C23C2×D4×D4311yescharacteristic
566D4—22no—
567D4—22no—
568D4—48no—
569D4—41no—
570D4—41no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—432no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—861no—
600C2×C4—3444no—
601C2×C4—3444no—
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—1721no—
612C2×C4#1306330212yes—
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4C22×Dic8611yescharacteristic
615C2×C4C2×#1062190011yescharacteristic
616C2×C4C2×#1062190011yescharacteristic
617C2×C4#1306337111yescharacteristic
618C2×C4#1306337211yescharacteristic
619C8—22no—
620C8—22no—
621C8—1721no—
622C8—1721no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22C2×#1306330211yescharacteristic
638C22#1458353311yescharacteristic
639C22#1458354911yescharacteristic
640C22AGL(1,ℤ/8)×D4311yescharacteristic
641C22#1458369511yescharacteristic
642C22#1458370811yescharacteristic
643C22#1458370911yescharacteristic
644C4—22no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—862no—
649C4—3441no—
650C4—3441no—
651C4—1721no—
652C4—1721no—
653C4—1721no—
654C4—1722no—
655C4—1722no—
656C4#1458340511yescharacteristic
657C4#1458349311yescharacteristic
658C4D4×Dic8611yescharacteristic
659C4#1458360611yescharacteristic
660C2—42no—
661C2—82no—
662C2#1913841011yescharacteristic
663C2#1914438911yescharacteristic
664C2#1914446111yescharacteristic
665C2#1914618711yescharacteristic
666C2#1914619211yescharacteristic
667C2#1914706011yescharacteristic
668C2#1914715011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1895C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#1895D43
hypocenterC43#26366
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
1. C2×#14583197C2semidirect
2. C2×#14582941C2semidirect
3. #19138309C2semidirect
5. #19136126C2semidirect
6. #19136095C2semidirect
7. #19135981C2semidirect
8. #19135936C2semidirect
9. #19135357C2semidirect
10. #19135165C2semidirect
12. #19134858C2semidirect
13. #19134787C2semidirect
14. #19134778C2semidirect
97. #13063259D4semidirect
395. C43#26366semidirect

Maximal subgroups

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

subgroupindex
C2×#145831972
C2×#145829412
#191383092
#191376152
#191361262
#191360952
#191359812
#191359362
#191353572
#191351652
#191349182
#191348582
#191347872
#191347782
C43×#18952
#2636643