Finite Group Databasebeta

← #25112055

Subgroups — #25112055

Order 11008.

1490 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C43⋊C8C211yesmaximal, characteristic, complemented
2C2×#14582895C212yesmaximal, complemented
3#19137544C211yesmaximal, characteristic, complemented
4#19135519C211yesmaximal, characteristic, complemented
5#19135398C211yesmaximal, characteristic, complemented
6#19135019C212yesmaximal, complemented
7#19134908C212yesmaximal, complemented
8#19134595C211yesmaximal, characteristic, complemented
9#19134535C212yesmaximal, complemented
10C4×#13063246C211yesmaximal, characteristic, complemented
11C2×C43×#547C211yesmaximal, characteristic
12C23×C43⋊C8C2212yes—
13C2×#13063284C2212yes—
14D4×C43⋊C8—24no—
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16#14582895—28no—
17C2×#13063249C2212yes—
18C2×#13063249C2212yes—
19C2×#13063249C2212yes—
20C2×#13063249C2212yes—
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2212yes—
23C2×#13063246C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2212yes—
25C2×C4×C43⋊C8C2211yescharacteristic
26#14582802—21no—
27#14582792—22no—
28#14582769C2211yescharacteristic
29#14582759C2212yes—
30C4⋊C4×Dic43—21no—
31C4×C4⋊Dic43C2211yescharacteristic
32#14582661C2211yescharacteristic
33#14582661C2212yes—
34#14582661C2211yescharacteristic
35C22×#41×C43C2212yes—
36C43×#547—24no—
37C43×#547C418yescomplemented
38C2×C4⋊Q8×C43C2211yescharacteristic
39C2×#123×C43—22no—
40C2×C22⋊Q8×C43C2212yes—
41C2×#121×C43—21no—
42C2×C4×D4×C43C2211yescharacteristic
43C2×C4×D4×C43C2211yescharacteristic
44C22×C4⋊C4×C43—21no—
45C22×C43⋊C8—24no—
46C22×C43⋊C8—24no—
47C22×C43⋊C8—42no—
48C22×C43⋊C8C2311yescharacteristic
49C22×C43⋊C8C2312yes—
50C22×C43⋊C8C2311yescharacteristic
51#13063284—24no—
52#13063284—42no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43C2312yes—
56C2×C4⋊Dic43C2311yescharacteristic
57C2×C4⋊Dic43C2311yescharacteristic
58C2×C22⋊Dic43—22no—
59C2×C22⋊Dic43—22no—
60C2×C4×Dic43—22no—
61C2×C4×Dic43—21no—
62C4⋊(C43⋊C8)—22no—
63#13063249—24no—
64#13063249—24no—
65#13063249—42no—
66#13063249—42no—
67#13063246—24no—
68#13063246—22no—
69#13063246D414yescomplemented
70C22⋊(C43⋊C8)—24no—
71C4×C43⋊C8—22no—
72C43⋊#95—21no—
73C43⋊#95—22no—
74C2×#41×C43—24no—
75C2×#41×C43—24no—
76C2×#41×C43—24no—
77C2×#41×C43—42no—
78C2×#41×C43—42no—
79C2×#41×C43C2×C418yes—
80C22×Q8×C43C2312yes—
81C22×D4×C43—22no—
82C22×D4×C43D411yescharacteristic
83C22×D4×C43C2311yescharacteristic
84C23×C4×C43—21no—
85C23×C4×C43—22no—
86C23×C4×C43C2312yes—
87C4⋊Q8×C43—22no—
88C4⋊Q8×C43C2×C414yes—
89#123×C43—216no—
90C22⋊Q8×C43—24no—
91C22⋊Q8×C43C2×C418yes—
92#121×C43—28no—
93C4×D4×C43—22no—
94C4×D4×C43C2×C414yes—
95C4×D4×C43C2×C414yes—
96C4×D4×C43D414yes—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—28no—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C22⋊C4×C43—22no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43D412yes—
106C2×C42×C43C2311yescharacteristic
107C24×C43—21no—
108C24×C43C2×D412yes—
109#41×C43—216no—
110#41×C43—48no—
111#41×C43—48no—
112#41×C43—48no—
113C2×Q8×C43—22no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43C22×C414yes—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—28no—
125C2×D4×C43—44no—
126C2×D4×C43—44no—
127C2×D4×C43C22⋊C414yes—
128C2×D4×C43C22×C412yes—
129C2×D4×C43C2×D412yes—
130C2×D4×C43#4112yes—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—24no—
136C22×C4×C43—28no—
137C22×C4×C43—21no—
138C22×C4×C43—22no—
139C22×C4×C43—44no—
140C22×C4×C43—44no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43C22×C414yes—
144C22×C4×C43C2×D414yes—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D412yes—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—22no—
152C4⋊C4×C43—24no—
153C4⋊C4×C43—28no—
154C4⋊C4×C43—24no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43C22⋊C414yes—
157C4⋊C4×C43C22×C412yes—
158C22⋊C4×C43—24no—
159C22⋊C4×C43—28no—
160C22⋊C4×C43C22⋊C418yes—
161C42×C43C22×C412yes—
162C42×C43C2×D412yes—
163C22⋊Dic43—44no—
164C22⋊Dic43—82no—
165C4⋊Dic43—21no—
166C4⋊Dic43—22no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—22no—
170C4⋊Dic43—42no—
171C4⋊Dic43—81no—
172C4⋊Dic43C2×D412yes—
173C4×Dic43—44no—
174C4×Dic43—42no—
175C2×C43⋊C8—21no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—21no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—48no—
184C2×C43⋊C8C2×D412yes—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43C2×C22⋊C414yes—
199C23×C43C22×D411yescharacteristic
200Q8×C43—24no—
201Q8×C43—24no—
202Q8×C43—42no—
203Q8×C43—42no—
204D4×C43—22no—
205D4×C43—22no—
206D4×C43—22no—
207D4×C43—28no—
208D4×C43—416no—
209D4×C43C4×D414yes—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—22no—
219C2×C4×C43—24no—
220C2×C4×C43—416no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—48no—
226C2×C4×C43C2×C22⋊C412yes—
227C2×C4×C43C2×C22⋊C414yes—
228C2×C4×C43C2×C22⋊C412yes—
229C2×C4×C43#13512yes—
230C2×C4×C43#13512yes—
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×Dic43—22no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—42no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—41no—
246C43⋊C8—22no—
247C43⋊C8—42no—
248C43⋊C8—41no—
249#22417—431nomaximal, Sylow
250C22×C43—24no—
251C22×C43—24no—
252C22×C43—24no—
253C22×C43—24no—
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43C22×C22⋊C411yescharacteristic
265C22×C43D4211yescharacteristic
266C22×C43#54611yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×#13511yescharacteristic
269C22×C43#57711yescharacteristic
270C22×C43#57811yescharacteristic
271C4×C43—24no—
272C4×C43—22no—
273C4×C43—44no—
274C4×C43—42no—
275C4×C43#41614yescomplemented
276C4×C43C2×C4×D411yescharacteristic
277C4×C43#51811yescharacteristic
278C4×C43D4211yescharacteristic
279C4×C43#54611yescharacteristic
280Dic43—42no—
281Dic43—82no—
282Dic43—81no—
283C2×#547D4311yescharacteristic
284C2×C8×D4—431no—
285C2×#416—432no—
286#2354—431no—
287#1981—431no—
288#1956—431no—
289#1892—432no—
290#1873—432no—
291#1802—431no—
292#1788—432no—
293C4×#102—431no—
294C2×C43—44no—
295C2×C43—44no—
296C2×C43D4×C22⋊C411yescharacteristic
297C2×C43C2×#41611yescharacteristic
298C2×C43#289811yescharacteristic
299C2×C43#328311yescharacteristic
300C2×C43#328411yescharacteristic
301C2×C43#330211yescharacteristic
302C2×C43#330311yescharacteristic
303C22×#41C2×D4312yes—
304C23×C8—432no—
305#547—24no—
306#547Dic4318yescomplemented
307C2×C4⋊Q8C2×D4311yescharacteristic
308C2×#123—22no—
309C2×C22⋊Q8C2×D4312yes—
310C2×#121—21no—
311C2×C4×D4C2×D4311yescharacteristic
312C2×C4×D4C2×D4311yescharacteristic
313C2×#117—432no—
314C22×C4⋊C4—21no—
315C8×D4—864no—
316C2×C4⋊C8—431no—
317#416—868no—
318C2×#103—432no—
319C2×#103—432no—
320C2×#103—432no—
321C2×#103—432no—
322C2×#102—431no—
323C2×#102—432no—
324C2×#102—431no—
325C2×C22⋊C8—432no—
326C2×C4×C8—431no—
327#390—861no—
328#388—862no—
329#384—431no—
330#380—432no—
331C4×C4⋊C4—431no—
332C4×C4⋊C4—861no—
333#340—432no—
334#340—431no—
335#340—431no—
336C43#2241711yescharacteristic, complemented, Sylow
337C2×#41—24no—
338C2×#41—24no—
339C2×#41—24no—
340C2×#41—42no—
341C2×#41—42no—
342C2×#41C2×Dic4318yes—
343C22×Q8C22×D4312yes—
344C22×D4—22no—
345C22×D4C22⋊D4311yescharacteristic
346C22×D4C22×D4311yescharacteristic
347C23×C4—21no—
348C23×C4—22no—
349C23×C4C22×D4312yes—
350C22×C8—431no—
351C22×C8—432no—
352C22×C8—431no—
353C22×C8—864no—
354C22×C8—864no—
355C22×C8—1722no—
356C4⋊Q8—22no—
357C4⋊Q8C2×Dic4314yes—
358#123—216no—
359C22⋊Q8—24no—
360C22⋊Q8C2×Dic4318yes—
361#121—28no—
362C4×D4—22no—
363C4×D4C2×Dic4314yes—
364C4×D4C2×Dic4314yes—
365C4×D4C22⋊D4314yes—
366#117—864no—
367#117—1722no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—432no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4C22⋊D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—862no—
382C2×C22⋊C4—862no—
383C2×C22⋊C4C22⋊D4312yes—
384C2×C42—862no—
385C2×C42—861no—
386C2×C42C22×D4311yescharacteristic
387C4⋊C8—862no—
388#103—864no—
389#103—864no—
390#103—1722no—
391#103—1722no—
392#102—434no—
393#102—864no—
394#102—862no—
395C22⋊C8—864no—
396C4×C8—862no—
397#95—861no—
398#95—862no—
399C24—21no—
400C24C2×C22⋊D4312yes—
401#41—216no—
402#41—48no—
403#41—48no—
404#41—48no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8C22×Dic4314yes—
411C2×D4—28no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4C22⋊Dic4314yes—
420C2×D4D4×D4312yes—
421C2×D4#1062190012yes—
422C2×D4C22×Dic4312yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—28no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—862no—
438C22×C4C22×Dic4314yes—
439C22×C4C2×C22⋊D4312yes—
440C22×C4C2×C22⋊D4311yescharacteristic
441C22×C4C2×C22⋊D4314yes—
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—432no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—862no—
448C2×C8—861no—
449C2×C8—862no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—862no—
453C2×C8—1728no—
454C4⋊C4—24no—
455C4⋊C4—28no—
456C4⋊C4—24no—
457C4⋊C4—21no—
458C4⋊C4—432no—
459C4⋊C4—861no—
460C4⋊C4—862no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—862no—
464C4⋊C4—3441no—
465C4⋊C4—1722no—
466C4⋊C4C22⋊Dic4314yes—
467C4⋊C4C22×Dic4312yes—
468C22⋊C4—28no—
469C22⋊C4—24no—
470C22⋊C4—3442no—
471C22⋊C4—1724no—
472C22⋊C4C22⋊Dic4318yes—
473C42—1724no—
474C42—1722no—
475C42C22×Dic4312yes—
476C42C2×C22⋊D4312yes—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C2×C22⋊Dic4314yes—
491C23C22×C22⋊D4311yescharacteristic
492Q8—24no—
493Q8—24no—
494Q8—42no—
495Q8—42no—
496D4—22no—
497D4—28no—
498D4—22no—
499D4—22no—
500D4—416no—
501D4D4×Dic4314yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—416no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—48no—
518C2×C4—862no—
519C2×C4—1721no—
520C2×C4—1722no—
521C2×C4—1721no—
522C2×C4—1722no—
523C2×C4—1722no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4C2×C22⋊Dic4312yes—
528C2×C4C2×C22⋊Dic4314yes—
529C2×C4C2×C22⋊Dic4312yes—
530C2×C4#1306334512yes—
531C2×C4#1306334512yes—
532C2×C4C23×Dic4311yescharacteristic
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C22×C22⋊D4311yescharacteristic
535C2×C4C2×#1062190011yescharacteristic
536C2×C4#1306337011yescharacteristic
537C2×C4#1306337011yescharacteristic
538C8—862no—
539C8—1722no—
540C8—1721no—
541C22—24no—
542C22—24no—
543C22—24no—
544C22—24no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22C22×C22⋊Dic4311yescharacteristic
556C22D4×C22⋊D4311yescharacteristic
557C22#1458354311yescharacteristic
558C22C2×#1306334511yescharacteristic
559C22C2×#1306334511yescharacteristic
560C22#1458370711yescharacteristic
561C22#1458371411yescharacteristic
562C4—24no—
563C4—22no—
564C4—44no—
565C4—42no—
566C4—3441no—
567C4—3442no—
568C4—1722no—
569C4#1458289514yescomplemented
570C4C2×D4×Dic4311yescharacteristic
571C4#1458337411yescharacteristic
572C4D4×C22⋊D4311yescharacteristic
573C4#1458354311yescharacteristic
574C2—44no—
575C2—44no—
576C2D4×C22⋊Dic4311yescharacteristic
577C2C2×#1458289511yescharacteristic
578C2#1914312811yescharacteristic
579C2#1914631311yescharacteristic
580C2#1914632111yescharacteristic
581C2#1914651211yescharacteristic
582C2#1914652311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#547C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#547D43
hypocenterC43#22417
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×D4×C43⋊C8C2semidirect
2. C2×#14582895C2semidirect
3. #19137544C2semidirect
4. #19135519C2semidirect
5. #19135398C2semidirect
6. #19135019C2semidirect
7. #19134908C2semidirect
8. #19134595C2semidirect
9. #19134535C2semidirect
10. C4×#13063246C2semidirect
37. C43×#547C4semidirect
69. #13063246D4semidirect
275. C4×C43#416semidirect
306. #547Dic43semidirect
336. C43#22417semidirect
569. C4#14582895semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C43⋊C82
C2×#145828952
#191375442
#191355192
#191353982
#191350192
#191349082
#191345952
#191345352
C4×#130632462
C2×C43×#5472
#2241743