Finite Group Databasebeta

← #25013539

Subgroups — #25013539

Order 11008.

582 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583136C211yesmaximal, characteristic
2C2×#14582936C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic, complemented
5C2×(C2×D43)⋊C16C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C43×#1380C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C22×C8×D43C2211yescharacteristic
10C2×#13063300—21no—
11C2×#13063283—21no—
12C22×C43⋊C16C2211yescharacteristic
13#14583136—22no—
14#14583136C414yescomplemented
15#14582936—22no—
16#14582936—22no—
17C2×#13063259C2211yescharacteristic
18C2×#13063256—21no—
19C2×#13063245—21no—
20#14582701—22no—
21#14582699—22no—
22(C2×D43)⋊C16—22no—
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C2×#107×C43C2211yescharacteristic
26C22×D172—21no—
27C22×D172—41no—
28C22×C4×D43D411yescharacteristic
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344C2×C412yes—
35C22×C43⋊C8D411yescharacteristic
36C2×C8×D43—21no—
37C2×C8×D43—21no—
38C2×C8×D43—21no—
39C2×C8×D43—21no—
40C2×C8×D43C2×C412yes—
41C2×C8×D43D412yes—
42#13063300—24no—
43#13063300—42no—
44#13063283—24no—
45#13063283—42no—
46C2×C4⋊Dic43—21no—
47C2×(C2×D43)⋊C4—41no—
48C2×(C2×D43)⋊C4—41no—
49C2×C4×Dic43—41no—
50C2×C43⋊C16—21no—
51C2×C43⋊C16—21no—
52C2×C43⋊C16—21no—
53#13063259—21no—
54#13063259D412yescomplemented
55#13063256—24no—
56#13063245—24no—
57C22×C8×C43C2311yescharacteristic
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C16×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43—21no—
63#107×C43—21no—
64#107×C43—21no—
65#107×C43C2×C412yes—
66#107×C43D412yescomplemented
67C23×D43—41no—
68C23×D43D811yescharacteristic
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—41no—
73C22×Dic43D811yescharacteristic
74C2×D172—22no—
75C2×D172—41no—
76C2×D172—44no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—82no—
82C2×D172—82no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43C22⋊C412yes—
88C2×C4×D43SD1612yes—
89C2×C8×C43C22×C411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43C2×D411yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C2×C8×C43#4111yescharacteristic
95C4⋊C4×C43—22no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99(C2×D43)⋊C4—44no—
100(C2×D43)⋊C4—44no—
101C4⋊Dic43—22no—
102C4⋊Dic43—41no—
103C4×Dic43—44no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8C22⋊C412yes—
107D344—22no—
108D344—22no—
109D344—41no—
110D344—41no—
111C8×D43—22no—
112C8×D43—22no—
113C8×D43—22no—
114C8×D43—22no—
115C16×C43—41no—
116C43⋊C16—41no—
117C23×C43C2×D811yescharacteristic
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—42no—
125C22×D43—81no—
126C22×D43—81no—
127C22×D43—81no—
128C22×D43—81no—
129C22×D43—81no—
130C22×D43—81no—
131C22×D43#10212yes—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43C2×C22⋊C411yescharacteristic
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12311yescharacteristic
141C2×C4×C43C2×SD1611yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C43#13711yescharacteristic
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—42no—
147C2×Dic43—81no—
148C2×Dic43—81no—
149C2×Dic43#10212yes—
150D172—42no—
151D172—42no—
152D172—88no—
153D172—81no—
154D172—81no—
155C4×D43—22no—
156C4×D43—22no—
157C4×D43—22no—
158C4×D43—22no—
159C8×C43C4×D411yescharacteristic
160C8×C43C4×D411yescharacteristic
161C8×C43#12111yescharacteristic
162C8×C43#12111yescharacteristic
163C43⋊C8—22no—
164#12992—431nomaximal, Sylow
165C22×C43C2×#10211yescharacteristic
166C22×C43#44711yescharacteristic
167C22×C43#48011yescharacteristic
168C22×C43#50811yescharacteristic
169C22×C43#50811yescharacteristic
170C22×C43#50911yescharacteristic
171C22×C43#50911yescharacteristic
172C2×D43—22no—
173C2×D43—22no—
174C2×D43—22no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—82no—
180C2×D43—82no—
181C2×D43—82no—
182C2×D43—161no—
183C2×D43—161no—
184C2×D43—161no—
185C2×D43—161no—
186C4×C43—82no—
187C4×C43—82no—
188C4×C43#38611yescharacteristic
189C4×C43#41711yescharacteristic
190C4×C43#44811yescharacteristic
191C4×C43#48111yescharacteristic
192Dic43—22no—
193Dic43—82no—
194C2×#466—431no—
195C2×#427—431no—
196C2×#357—431no—
197C2×#357—431no—
198C2×C22⋊C16—431no—
199#1380—431no—
200#1380D4311yescharacteristic, complemented
201C2×C43#187411yescharacteristic
202C2×C43#213811yescharacteristic
203C2×C43#214011yescharacteristic
204C2×C43#218611yescharacteristic
205C2×C43#218611yescharacteristic
206C2×C43#223411yescharacteristic
207C2×C43#223411yescharacteristic
208D43—42no—
209D43—162no—
210C22×D8—431no—
211C23×C8—431no—
212C2×#121—861no—
213C2×#117—861no—
214C22×C16—431no—
215C22×C16C2×D4311yescharacteristic
216#466—434no—
217#466—862no—
218#427—862no—
219#427—862no—
220C2×#107—431no—
221C2×#107C2×D4311yescharacteristic
222C2×#107C2×D4311yescharacteristic
223C2×#106—861no—
224C2×#102—861no—
225#357—862no—
226#357—862no—
227C22⋊C16—862no—
228C43#1299211yescharacteristic, complemented, Sylow
229C22×D4—861no—
230C22×D4—1721no—
231C23×C4—431no—
232C2×D8—432no—
233C2×D8—861no—
234C2×D8—861no—
235C2×D8—861no—
236C2×D8—861no—
237C2×D8—861no—
238C22×C8—431no—
239C22×C8—432no—
240C22×C8—432no—
241C22×C8—861no—
242C22×C8—861no—
243C22×C8—861no—
244C22×C8—861no—
245C22×C8C22×D4311yescharacteristic
246#121—864no—
247#121—1722no—
248#117—864no—
249#117—1722no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—861no—
253C2×C22⋊C4—1721no—
254C2×C22⋊C4—1721no—
255C2×C42—1721no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16—861no—
260C2×C16—861no—
261C2×C16—861no—
262#107—21no—
263#107—21no—
264#107—432no—
265#107—861no—
266#107C4×D4312yes—
267#107D17212yescomplemented
268#106—864no—
269#102—864no—
270C24—431no—
271C24—1721no—
272C2×D4—862no—
273C2×D4—3442no—
274C2×D4—3442no—
275C2×D4—1724no—
276C2×D4—1721no—
277C2×D4—1721no—
278C2×D4—1721no—
279C2×D4—1721no—
280C2×D4—1721no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—431no—
284C22×C4—432no—
285C22×C4—432no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—1721no—
291C22×C4D4×D4311yescharacteristic
292D8—862no—
293D8—862no—
294D8—1721no—
295D8—1721no—
296C2×C8—432no—
297C2×C8—861no—
298C2×C8—861no—
299C2×C8—862no—
300C2×C8—862no—
301C2×C8—862no—
302C2×C8—862no—
303C2×C8C2×C4×D4311yescharacteristic
304C2×C8C2×D17211yescharacteristic
305C2×C8#1062189811yescharacteristic
306C2×C8D4×D4311yescharacteristic
307C2×C8D4×D4311yescharacteristic
308C2×C8#1062190211yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—862no—
314C4⋊C4—1721no—
315C22⋊C4—1724no—
316C22⋊C4—1724no—
317C42—1724no—
318C16—41no—
319C16—1721no—
320C23—432no—
321C23—861no—
322C23—861no—
323C23—861no—
324C23—861no—
325C23—861no—
326C23—861no—
327C23—3441no—
328C23—3441no—
329C23—3441no—
330C23—3441no—
331C23—3441no—
332C23—3441no—
333C23—1722no—
334C23D8×D4311yescharacteristic
335D4—3448no—
336D4—3441no—
337D4—3441no—
338D4—1722no—
339D4—1722no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—432no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4—862no—
352C2×C4—862no—
353C2×C4—3441no—
354C2×C4—3441no—
355C2×C4—1722no—
356C2×C4C22⋊C4×D4311yescharacteristic
357C2×C4#1306329511yescharacteristic
358C2×C4#1306331011yescharacteristic
359C2×C4SD16×D4311yescharacteristic
360C2×C4#1306335211yescharacteristic
361C2×C4#1306335711yescharacteristic
362C8—862no—
363C8#1306328711yescharacteristic
364C8C4×D17211yescharacteristic
365C8#1306329811yescharacteristic
366C8#1306330011yescharacteristic
367C22—862no—
368C22—862no—
369C22—862no—
370C22—3442no—
371C22—3442no—
372C22—3442no—
373C22—1721no—
374C22—1721no—
375C22—1721no—
376C22—1721no—
377C22—6881no—
378C22—6881no—
379C22—6881no—
380C22—6881no—
381C22#102×D4311yescharacteristic
382C22#1458303411yescharacteristic
383C22#1458321411yescharacteristic
384C22#1458333011yescharacteristic
385C22#1458333211yescharacteristic
386C22#1458333311yescharacteristic
387C22#1458333611yescharacteristic
388C4—82no—
389C4—82no—
390C4—862no—
391C4—3442no—
392C4#1458277711yescharacteristic
393C4#1458289911yescharacteristic
394C4#1458303911yescharacteristic
395C4#1458321911yescharacteristic
396C2—1722no—
397C2—6882no—
398C2#1913491111yescharacteristic
399C2#1913630111yescharacteristic
400C2#1913630911yescharacteristic
401C2#1913651911yescharacteristic
402C2#1913652111yescharacteristic
403C2#1913678811yescharacteristic
404C2#1913678911yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1380C2
socleC23×C43C2×D8
prime radicalC2×#14583136C2
cosocleC22×C8×C43C23
hypercenter#1380D43
hypocenterC43#12992
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#14582936C2semidirect
3. C2×#14582701C2semidirect
4. C2×#14582699C2semidirect
5. C2×(C2×D43)⋊C16C2semidirect
6. #19132686C2semidirect
7. C43×#1380C2semidirect
14. #14583136C4semidirect
54. #13063259D4semidirect
66. #107×C43D4semidirect
200. #1380D43semidirect
228. C43#12992semidirect
267. #107D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145831362
C2×#145829362
C2×#145827012
C2×#145826992
C2×(C2×D43)⋊C162
#191326862
C43×#13802
#1299243