Finite Group Databasebeta

← #24998914

Subgroups — #24998914

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583179C211yesmaximal, characteristic, complemented
2C2×#14583105C211yesmaximal, characteristic, complemented
3#19139508C211yesmaximal, characteristic
4#19135556C211yesmaximal, characteristic, complemented
5C2×#14582628C211yesmaximal, characteristic, complemented
6#19132479C211yesmaximal, characteristic, complemented
7C2×C43×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×#10621873—21no—
9C2×#13063325C2211yescharacteristic
10C2×#13063299—21no—
11C2×#13063296—21no—
12C2×C4×D172C2211yescharacteristic
13#14583179—22no—
14#14583179—22no—
15#14583105—22no—
16#14583105—22no—
17C2×#13063258—21no—
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×#13063250—21no—
20C2×#13063246—21no—
21#14582815—22no—
22#14582769C2211yescharacteristic
23#14582759—21no—
24#14582756—21no—
25#14582662—22no—
26#14582628—22no—
27C2×C4×D4×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C43×D4⋊C8—22no—
31C22×Dic86—21no—
32C22×D172D411yescharacteristic
33C22×C22⋊D43—22no—
34C22×C4×D43—21no—
35C2×#10621873—24no—
36C2×#10621873—42no—
37C2×#10621873—42no—
38C22×C43⋊C8—21no—
39#13063325—21no—
40#13063325—21no—
41#13063325—21no—
42#13063325D412yescomplemented
43#13063299—42no—
44#13063299—42no—
45#13063296—42no—
46#13063296—42no—
47C4×D172—21no—
48C4×D172—21no—
49C4×D172—21no—
50C4×D172—21no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43D411yescharacteristic
56C2×C4⋊Dic43D412yes—
57C2×C22⋊Dic43—22no—
58C2×(C2×D43)⋊C4—22no—
59C2×(C2×D43)⋊C4—21no—
60#13063258—24no—
61C4⋊(C43⋊C8)—21no—
62C4⋊(C43⋊C8)D412yescomplemented
63#13063250—24no—
64#13063246—24no—
65C43⋊#95—22no—
66C22×D4×C43D411yescharacteristic
67C23×C4×C43—21no—
68C22×C8×C43—21no—
69C22×C8×C43—21no—
70C4×D4×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C22⋊C4×C43—21no—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43—21no—
78C4⋊C8×C43D412yescomplemented
79C4×C8×C43—21no—
80C4×C8×C43—21no—
81C24×C43—21no—
82C23×D43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43SD1612yescomplemented
89C22×C4×C43—21no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C2×C22⋊D43—44no—
100C2×C22⋊D43—44no—
101C2×C22⋊D43—82no—
102C22×Dic43—21no—
103C22×Dic43—22no—
104C22×Dic43—41no—
105C2×D172—21no—
106C2×D172—21no—
107C2×D172—21no—
108C2×D172—21no—
109C2×D172—21no—
110C2×D172D812yes—
111C2×C4×D43—41no—
112C2×C4×D43—41no—
113C2×C4×D43—41no—
114C2×C4×D43—41no—
115C2×C4×D43—41no—
116C2×C4×D43—41no—
117C2×Dic86—22no—
118C2×Dic86—41no—
119C2×Dic86—41no—
120C2×Dic86—41no—
121C2×Dic86—41no—
122C2×Dic86—41no—
123C2×C8×C43—22no—
124C2×C8×C43—22no—
125C2×C8×C43—41no—
126C2×C8×C43—41no—
127C2×C8×C43—41no—
128C2×C8×C43—41no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C22⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C42×C43C2×D411yescharacteristic
134C42×C43C2×D411yescharacteristic
135C42×C43C2×D411yescharacteristic
136C42×C43#4111yescharacteristic
137C22⋊Dic43—44no—
138(C2×D43)⋊C4—44no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4—41no—
141C4⋊Dic43—22no—
142C4⋊Dic43—21no—
143C4⋊Dic43—22no—
144C4⋊Dic43—21no—
145C4⋊Dic43—41no—
146C4⋊Dic43—41no—
147C4⋊Dic43—41no—
148C4⋊Dic43—41no—
149C4⋊Dic43—41no—
150C4⋊Dic43—41no—
151C4⋊Dic43—42no—
152C2×C43⋊C8—22no—
153C2×C43⋊C8—41no—
154C2×C43⋊C8—41no—
155#10621873—48no—
156C23×C43—22no—
157C23×C43—41no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43—41no—
161C23×C43—41no—
162C23×C43—41no—
163C23×C43#12011yescharacteristic
164C22×D43—22no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171D4×C43—22no—
172D4×C43—22no—
173D4×C43—41no—
174D4×C43—41no—
175C2×C4×C43—21no—
176C2×C4×C43—21no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—81no—
181C2×C4×C43—81no—
182C2×C4×C43—81no—
183C2×C4×C43—81no—
184C2×C4×C43#12011yescharacteristic
185C2×C4×C43#12011yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12711yescharacteristic
190C2×C4×C43C2×D811yescharacteristic
191C2×C4×C43C2×SD1611yescharacteristic
192C2×C4×C43#13511yescharacteristic
193C2×C4×C43#13511yescharacteristic
194C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C43#13711yescharacteristic
198C22⋊D43—88no—
199C2×Dic43—42no—
200C2×Dic43—41no—
201C2×Dic43—42no—
202C2×Dic43—42no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—42no—
206C2×Dic43—81no—
207C2×Dic43—81no—
208D172—22no—
209D172—22no—
210D172—41no—
211D172—41no—
212C4×D43—81no—
213C4×D43—81no—
214C4×D43—81no—
215C4×D43—81no—
216Dic86—42no—
217Dic86—42no—
218Dic86—81no—
219Dic86—81no—
220C8×C43—42no—
221C8×C43—42no—
222C43⋊C8—42no—
223#10231—431nomaximal, Sylow
224C22×C43—42no—
225C22×C43—42no—
226C22×C43—42no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43—81no—
230C22×C43—81no—
231C22×C43#39211yescharacteristic
232C22×C43#44711yescharacteristic
233C22×C43#44911yescharacteristic
234C22×C43#45011yescharacteristic
235C22×C43#45211yescharacteristic
236C22×C43#45511yescharacteristic
237C22×C43#45611yescharacteristic
238C2×D43—42no—
239C2×D43—42no—
240C2×D43—42no—
241C2×D43—81no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—81no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—81no—
248C4×C43#44711yescharacteristic
249C4×C43#44811yescharacteristic
250C4×C43#44911yescharacteristic
251C4×C43#44911yescharacteristic
252C4×C43#46511yescharacteristic
253C4×C43#46611yescharacteristic
254C4×C43#46811yescharacteristic
255C4×C43#46911yescharacteristic
256Dic43—82no—
257Dic43—82no—
258Dic43—81no—
259C2×#474—431no—
260C2×#461—431no—
261#2537—431no—
262#1990—431no—
263C2×D4⋊C8—431no—
264C2×D4⋊C8D4311yescharacteristic, complemented
265#1296—431no—
266C2×C43—82no—
267C2×C43#163911yescharacteristic
268C2×C43#164611yescharacteristic
269C2×C43#164711yescharacteristic
270C2×C43#165411yescharacteristic
271C2×C43#199911yescharacteristic
272C2×C43#200011yescharacteristic
273C2×C43#200711yescharacteristic
274D43—82no—
275C22×SD16—861no—
276C2×C4⋊Q8—431no—
277C2×#121—861no—
278C2×#121—861no—
279C2×C4×D4—431no—
280C2×C4×D4C2×D4311yescharacteristic
281#474—862no—
282#474—862no—
283#461—862no—
284#461—862no—
285C2×#107—861no—
286C2×C4⋊C8—431no—
287C2×C4⋊C8C2×D4311yescharacteristic
288C2×#103—861no—
289C2×#102—861no—
290C2×C4×C8C2×D4311yescharacteristic
291#394—862no—
292#384—431no—
293#380—861no—
294#380—861no—
295#340—862no—
296D4⋊C8—22no—
297D4⋊C8—862no—
298C43#1023111yescharacteristic, complemented, Sylow
299C22×Q8—861no—
300C22×D4—431no—
301C22×D4—862no—
302C22×D4D17211yescharacteristic
303C23×C4—21no—
304C23×C4—861no—
305C2×SD16—864no—
306C2×SD16—1722no—
307C2×SD16—1722no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—861no—
311C4⋊Q8—432no—
312C4⋊Q8—861no—
313C4⋊Q8—861no—
314C4⋊Q8—861no—
315#121—1722no—
316#121—1722no—
317#121—1722no—
318#121—1722no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—861no—
324C4×D4—861no—
325C4×D4—861no—
326C4×D4—861no—
327C2×C4⋊C4—431no—
328C2×C4⋊C4—432no—
329C2×C4⋊C4—861no—
330C2×C4⋊C4—861no—
331C2×C4⋊C4—861no—
332C2×C4⋊C4—861no—
333C2×C4⋊C4D17211yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—862no—
336C2×C22⋊C4—862no—
337C2×C22⋊C4—861no—
338C2×C42C22×D4311yescharacteristic
339#107—864no—
340C4⋊C8—21no—
341C4⋊C8—432no—
342C4⋊C8—861no—
343C4⋊C8C22⋊D4312yescomplemented
344#103—864no—
345#102—864no—
346C4×C8—21no—
347C4×C8—21no—
348#95—862no—
349C24—21no—
350C24—861no—
351C2×Q8—862no—
352C2×Q8—1721no—
353C2×Q8—1721no—
354C2×Q8—1721no—
355C2×Q8—1721no—
356C2×Q8—1721no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—432no—
363C2×D4—861no—
364C2×D4—861no—
365C2×D4—861no—
366C2×D4—861no—
367C2×D4—861no—
368C2×D4—3442no—
369C2×D4—1724no—
370C2×D4—1724no—
371C2×D4#1062187312yescomplemented
372C22×C4—21no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—861no—
380C22×C4—862no—
381C22×C4—1721no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4—1721no—
385C22×C4—1721no—
386C22×C4—1721no—
387C22×C4—1721no—
388C22×C4C2×D17211yescharacteristic
389C22×C4D4×D4311yescharacteristic
390C22×C4D4×D4311yescharacteristic
391SD16—1728no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—41no—
398C2×C8—862no—
399C2×C8—1721no—
400C2×C8—1721no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—861no—
404C4⋊C4—862no—
405C4⋊C4—861no—
406C4⋊C4—862no—
407C4⋊C4—1722no—
408C4⋊C4—1721no—
409C4⋊C4—1721no—
410C4⋊C4—1721no—
411C4⋊C4—1721no—
412C4⋊C4—1721no—
413C4⋊C4—1721no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—1724no—
417C22⋊C4—1724no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C42#1062189811yescharacteristic
421C42D4×D4311yescharacteristic
422C42D4×D4311yescharacteristic
423C42C2×C22⋊D4311yescharacteristic
424C23—22no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—862no—
432C23—1721no—
433C23—1721no—
434C23—1721no—
435C23—1721no—
436C23—1721no—
437C23—1721no—
438C23#1306329511yescharacteristic
439Q8—3441no—
440Q8—3441no—
441Q8—1722no—
442Q8—1722no—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447D4—862no—
448D4—862no—
449D4—3448no—
450D4—1721no—
451D4—1721no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—3441no—
462C2×C4—3441no—
463C2×C4—3441no—
464C2×C4—3441no—
465C2×C4—3441no—
466C2×C4—3441no—
467C2×C4—1721no—
468C2×C4—1722no—
469C2×C4—1721no—
470C2×C4—1721no—
471C2×C4—1722no—
472C2×C4—1722no—
473C2×C4—1722no—
474C2×C4#1306329311yescharacteristic
475C2×C4#1306329511yescharacteristic
476C2×C4#1306329811yescharacteristic
477C2×C4#1306329811yescharacteristic
478C2×C4#1306329911yescharacteristic
479C2×C4#1306332111yescharacteristic
480C2×C4D8×D4311yescharacteristic
481C2×C4C2×#1062187311yescharacteristic
482C2×C4#1306334611yescharacteristic
483C2×C4#1306334711yescharacteristic
484C2×C4#1306334911yescharacteristic
485C2×C4#1306335211yescharacteristic
486C2×C4#1306335311yescharacteristic
487C2×C4#1306335811yescharacteristic
488C8—42no—
489C8—42no—
490C8—1722no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—3441no—
499C22—3441no—
500C22—3441no—
501C22—3441no—
502C22—1722no—
503C22—1722no—
504C22—1722no—
505C22#1458280811yescharacteristic
506C22#1458303411yescharacteristic
507C22#1458304511yescharacteristic
508C22#1458305211yescharacteristic
509C22#1458306311yescharacteristic
510C22#1458307811yescharacteristic
511C22#1458308311yescharacteristic
512C4—21no—
513C4—21no—
514C4—81no—
515C4—3442no—
516C4—3442no—
517C4—3441no—
518C4#1458303111yescharacteristic
519C4#1458304011yescharacteristic
520C4#1458304311yescharacteristic
521C4#1458304611yescharacteristic
522C4#1458312811yescharacteristic
523C4#1458313411yescharacteristic
524C4#1458314511yescharacteristic
525C4#1458315111yescharacteristic
526C2—82no—
527C2—3442no—
528C2#1913377711yescharacteristic
529C2#1913382611yescharacteristic
530C2#1913383311yescharacteristic
531C2#1913388211yescharacteristic
532C2#1913559211yescharacteristic
533C2#1913560011yescharacteristic
534C2#1913564311yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×D4⋊C8C2
socleC23×C43#120
prime radical#19139508C2
hypercenterC2×D4⋊C8D43
hypocenterC43#10231
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#14583179C2semidirect
2. C2×#14583105C2semidirect
4. #19135556C2semidirect
5. C2×#14582628C2semidirect
6. #19132479C2semidirect
7. C2×C43×D4⋊C8C2semidirect
42. #13063325D4semidirect
62. C4⋊(C43⋊C8)D4semidirect
78. C4⋊C8×C43D4semidirect
88. C2×D4×C43SD16semidirect
264. C2×D4⋊C8D43semidirect
298. C43#10231semidirect
343. C4⋊C8C22⋊D43semidirect
371. C2×D4#10621873semidirect

Maximal subgroups

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

subgroupindex
C2×#145831792
C2×#145831052
#191395082
#191355562
C2×#145826282
#191324792
C2×C43×D4⋊C82
#1023143