Finite Group Databasebeta

← #25013958

Subgroups — #25013958

Order 11008.

578 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C16×D43C211yesmaximal, characteristic, complemented
2C2×#14583136C211yesmaximal, characteristic
3C2×#14582701C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic, complemented
5#19134621C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C43×#1380C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C22×C8×D43C2211yescharacteristic
10C2×#13063300—21no—
11C22×C43⋊C16C2211yescharacteristic
12C2×C16×D43—22no—
13C2×C16×D43—22no—
14C2×C16×D43—22no—
15#14583136—22no—
16#14583136C414yescomplemented
17C2×#13063259C2211yescharacteristic
18C2×#13063245—21no—
19#14582756—21no—
20#14582701—22no—
21#14582699—22no—
22#14582661—21no—
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—
44C2×C4⋊Dic43—21no—
45C2×(C2×D43)⋊C4—41no—
46C2×(C2×D43)⋊C4—41no—
47C2×C43⋊C16—21no—
48C2×C43⋊C16—21no—
49C2×C43⋊C16D412yescomplemented
50C16×D43—28no—
51#13063259—21no—
52#13063259—21no—
53#13063245—24no—
54C43⋊#95—41no—
55C22×C8×C43C2311yescharacteristic
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C16×C43—21no—
59C2×C16×C43—21no—
60C2×C16×C43D412yescomplemented
61#107×C43—21no—
62#107×C43—21no—
63#107×C43—21no—
64#107×C43C2×C412yes—
65C23×D43—41no—
66C23×D43D811yescharacteristic
67C22×C4×C43—41no—
68C22×C4×C43—41no—
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—41no—
71C22×Dic43D811yescharacteristic
72C2×D172—22no—
73C2×D172—41no—
74C2×D172—44no—
75C2×D172—41no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—82no—
80C2×D172—82no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43C22⋊C412yes—
86C2×C4×D43SD1612yes—
87C2×C8×C43C22×C411yescharacteristic
88C2×C8×C43C2×D411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C4⋊C4×C43—22no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97(C2×D43)⋊C4—44no—
98(C2×D43)⋊C4—82no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101C2×C43⋊C8—21no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8C22⋊C412yes—
104D344—22no—
105D344—22no—
106D344—41no—
107D344—41no—
108C8×D43—22no—
109C8×D43—22no—
110C8×D43—22no—
111C8×D43—22no—
112C16×C43—22no—
113C43⋊C16—22no—
114C23×C43C2×D811yescharacteristic
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—42no—
120C22×D43—81no—
121C22×D43—81no—
122C22×D43—81no—
123C22×D43—81no—
124C22×D43—81no—
125C22×D43—81no—
126C22×D43#10212yes—
127C22×D43D1612yes—
128C22×D43SD3212yes—
129C2×C4×C43—42no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43C2×C22⋊C411yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43C2×SD1611yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—81no—
144C2×Dic43—81no—
145C2×Dic43—81no—
146C2×Dic43#10212yes—
147D172—42no—
148D172—42no—
149D172—88no—
150D172—81no—
151D172—81no—
152C4×D43—22no—
153C4×D43—22no—
154C4×D43—22no—
155C4×D43—22no—
156C8×C43C4×D411yescharacteristic
157C8×C43C4×D411yescharacteristic
158C8×C43#12011yescharacteristic
159C8×C43#12311yescharacteristic
160C43⋊C8—22no—
161#13059—431nomaximal, Sylow
162C22×C43C2×#10211yescharacteristic
163C22×C43#46611yescharacteristic
164C22×C43#46611yescharacteristic
165C22×C43C2×D1611yescharacteristic
166C22×C43C2×SD3211yescharacteristic
167C22×C43#50811yescharacteristic
168C22×C43#50811yescharacteristic
169C2×D43—22no—
170C2×D43—22no—
171C2×D43—22no—
172C2×D43—22no—
173C2×D43—22no—
174C2×D43—22no—
175C2×D43—82no—
176C2×D43—82no—
177C2×D43—82no—
178C2×D43—161no—
179C2×D43—161no—
180C2×D43—161no—
181C2×D43—161no—
182C2×D43#35714yescomplemented
183C4×C43—82no—
184C4×C43—161no—
185C4×C43#38611yescharacteristic
186C4×C43#41611yescharacteristic
187C4×C43#46511yescharacteristic
188C4×C43#46511yescharacteristic
189Dic43—22no—
190Dic43—161no—
191C23×C16—431no—
192C2×#466—431no—
193C2×#357—431no—
194C2×#357—431no—
195#1808—431no—
196#1380—431no—
197#1380D4311yescharacteristic, complemented
198C2×C43#189311yescharacteristic
199C2×C43C2×#35711yescharacteristic
200C2×C43#213811yescharacteristic
201C2×C43#221511yescharacteristic
202C2×C43#221511yescharacteristic
203C2×C43#221711yescharacteristic
204C2×C43#221711yescharacteristic
205D43—24no—
206D43—162no—
207C22×D8—431no—
208C23×C8—431no—
209C2×#121—861no—
210C22×C16—431no—
211C22×C16—862no—
212C22×C16—862no—
213C22×C16—862no—
214C22×C16C2×D4311yescharacteristic
215#466—434no—
216#466—862no—
217C2×#107—431no—
218C2×#107C2×D4311yescharacteristic
219C2×#107C2×D4311yescharacteristic
220C2×#102—861no—
221#380—861no—
222#357—862no—
223#357—862no—
224#340—861no—
225C43#1305911yescharacteristic, complemented, Sylow
226C22×D4—861no—
227C22×D4—1721no—
228C23×C4—431no—
229C2×D8—432no—
230C2×D8—861no—
231C2×D8—861no—
232C2×D8—861no—
233C2×D8—861no—
234C2×D8—861no—
235C22×C8—431no—
236C22×C8—432no—
237C22×C8—432no—
238C22×C8—861no—
239C22×C8—861no—
240C22×C8—861no—
241C22×C8—861no—
242C22×C8C22×D4311yescharacteristic
243#121—864no—
244#121—1722no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—861no—
248C2×C22⋊C4—1721no—
249C2×C22⋊C4—1721no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—432no—
253C2×C16—868no—
254C2×C16—861no—
255C2×C16—861no—
256C2×C16D17212yescomplemented
257#107—21no—
258#107—21no—
259#107—21no—
260#107—861no—
261#107—861no—
262#107C4×D4312yes—
263#102—864no—
264#95—1721no—
265C24—431no—
266C24—1721no—
267C2×D4—862no—
268C2×D4—3442no—
269C2×D4—3442no—
270C2×D4—1724no—
271C2×D4—1721no—
272C2×D4—1721no—
273C2×D4—1721no—
274C2×D4—1721no—
275C2×D4—1721no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—431no—
279C22×C4—432no—
280C22×C4—432no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—1721no—
286C22×C4D4×D4311yescharacteristic
287D8—862no—
288D8—862no—
289D8—1721no—
290D8—1721no—
291C2×C8—432no—
292C2×C8—861no—
293C2×C8—861no—
294C2×C8—862no—
295C2×C8—862no—
296C2×C8—862no—
297C2×C8—862no—
298C2×C8C2×C4×D4311yescharacteristic
299C2×C8C2×D17211yescharacteristic
300C2×C8#1062189811yescharacteristic
301C2×C8D4×D4311yescharacteristic
302C2×C8D4×D4311yescharacteristic
303C2×C8#1062190211yescharacteristic
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C22⋊C4—3442no—
311C22⋊C4—1724no—
312C16—22no—
313C16—862no—
314C23—432no—
315C23—432no—
316C23—432no—
317C23—861no—
318C23—861no—
319C23—861no—
320C23—861no—
321C23—3441no—
322C23—3441no—
323C23—3441no—
324C23—3441no—
325C23—3441no—
326C23—3441no—
327C23—1722no—
328C23D8×D4311yescharacteristic
329D4—3448no—
330D4—3441no—
331D4—3441no—
332D4—1722no—
333D4—1722no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—432no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—3441no—
348C2×C4—3441no—
349C2×C4—3441no—
350C2×C4C22⋊C4×D4311yescharacteristic
351C2×C4#1306329811yescharacteristic
352C2×C4#1306330011yescharacteristic
353C2×C4SD16×D4311yescharacteristic
354C2×C4#1306334611yescharacteristic
355C2×C4#1306334811yescharacteristic
356C8—862no—
357C8#1306328711yescharacteristic
358C8C4×D17211yescharacteristic
359C8#1306329511yescharacteristic
360C8#1306331011yescharacteristic
361C22—434no—
362C22—862no—
363C22—862no—
364C22—862no—
365C22—862no—
366C22—862no—
367C22—862no—
368C22—3442no—
369C22—3442no—
370C22—3442no—
371C22—6881no—
372C22—6881no—
373C22—6881no—
374C22—6881no—
375C22#102×D4311yescharacteristic
376C22#1458313411yescharacteristic
377C22#1458313611yescharacteristic
378C22D16×D4311yescharacteristic
379C22SD32×D4311yescharacteristic
380C22#1458333011yescharacteristic
381C22#1458333211yescharacteristic
382C4—82no—
383C4—161no—
384C4—862no—
385C4—6881no—
386C4#1458277711yescharacteristic
387C4#1458289411yescharacteristic
388C4#1458312911yescharacteristic
389C4#1458313111yescharacteristic
390C2—864no—
391C2—6882no—
392C2#1913502211yescharacteristic
393C2#357×D4311yescharacteristic
394C2#1913630111yescharacteristic
395C2#1913668011yescharacteristic
396C2#1913668211yescharacteristic
397C2#1913669211yescharacteristic
398C2#1913669411yescharacteristic
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#13059
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
1. C22×C16×D43C2semidirect
3. C2×#14582701C2semidirect
4. C2×#14582699C2semidirect
5. #19134621C2semidirect
6. #19132686C2semidirect
7. C43×#1380C2semidirect
16. #14583136C4semidirect
49. C2×C43⋊C16D4semidirect
60. C2×C16×C43D4semidirect
182. C2×D43#357semidirect
197. #1380D43semidirect
225. C43#13059semidirect
256. C2×C16D172semidirect

Maximal subgroups

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

subgroupindex
C22×C16×D432
C2×#145831362
C2×#145827012
C2×#145826992
#191346212
#191326862
C43×#13802
#1305943