Finite Group Databasebeta

← #25010175

Subgroups — #25010175

Order 11008.

320 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19136867C211yesmaximal, characteristic, complemented
2#19136640C211yesmaximal, characteristic, complemented
3#19134089C211yesmaximal, characteristic, complemented
4#19132638C211yesmaximal, characteristic, complemented
5#19132577C211yesmaximal, characteristic, complemented
6#19132562C211yesmaximal, characteristic, complemented
7C43×#3403C211yesmaximal, characteristic
8C2×#13063271—21no—
9C2×#13063269—21no—
10C2×#13063269—21no—
11#14583279C2211yescharacteristic
12#14583184—21no—
13C4⋊(C43⋊C16)C2211yescharacteristic
14#14582702—21no—
15#14582675C2211yescharacteristic
16#14582650C2211yescharacteristic
17#14582646—21no—
18C43×#559—21no—
19C43×#496—21no—
20C43×#495C2211yescharacteristic
21C43×#464—21no—
22C43×#463—21no—
23C43×#459—21no—
24C43×#446C2211yescharacteristic
25C43×#440—21no—
26C4×D8×C43C2211yescharacteristic
27C2×Dic172—21no—
28C2×Dic172—21no—
29#13063325—21no—
30#13063271—42no—
31#13063269—42no—
32#13063269—42no—
33C2×C43⋊C16—21no—
34C2×C43⋊C16—21no—
35#13063256—41no—
36C4⋊(C43⋊C8)—21no—
37#13063249—41no—
38C2×Q16×C43D411yescharacteristic
39C2×SD16×C43—21no—
40C2×SD16×C43—21no—
41C2×D8×C43—21no—
42C2×D8×C43D411yescharacteristic
43C2×D8×C43D411yescharacteristic
44#127×C43—21no—
45#124×C43—21no—
46#124×C43—21no—
47#124×C43—41no—
48#123×C43—41no—
49#123×C43—41no—
50C4×Q8×C43—21no—
51C4×Q8×C43D411yescharacteristic
52C4×D4×C43—21no—
53C4×D4×C43—21no—
54C4×D4×C43—41no—
55#107×C43D411yescharacteristic
56C4⋊C8×C43—21no—
57C4⋊C8×C43D411yescharacteristic
58#103×C43—21no—
59#102×C43—21no—
60#102×C43—21no—
61#97×C43—21no—
62C4×C8×C43C2311yescharacteristic
63C2×Q8×C43—21no—
64C2×Q8×C43D811yescharacteristic
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C2×Dic86—41no—
72Q16×C43—41no—
73SD16×C43—41no—
74SD16×C43—41no—
75SD16×C43—81no—
76D8×C43—21no—
77D8×C43—21no—
78D8×C43—41no—
79D8×C43—81no—
80C2×C8×C43—21no—
81C2×C8×C43C2×D411yescharacteristic
82C2×C8×C43C2×D411yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43D811yescharacteristic
87C22⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C42×C43—21no—
94C42×C43—41no—
95C42×C43C2×D411yescharacteristic
96C4⋊Dic43—41no—
97C4⋊Dic43—41no—
98C2×C43⋊C8—41no—
99Dic172—41no—
100Dic172—41no—
101Dic172—41no—
102Dic172—41no—
103C43⋊C16—22no—
104C43⋊C16—41no—
105C23×C43—41no—
106C23×C43—41no—
107Q8×C43—41no—
108Q8×C43—41no—
109Q8×C43—41no—
110D4×C43—41no—
111D4×C43—41no—
112D4×C43—41no—
113D4×C43—41no—
114D4×C43—82no—
115D4×C43—161no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—161no—
121C2×C4×C43—161no—
122C2×C4×C43#12011yescharacteristic
123C2×C4×C43C2×D811yescharacteristic
124C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
125C2×Dic43—81no—
126Dic86—81no—
127Dic86—81no—
128C8×C43—21no—
129C8×C43—41no—
130C8×C43#13511yescharacteristic
131C8×C43AGL(1,ℤ/8)11yescharacteristic
132C43⋊C8—81no—
133#12338—431nomaximal, Sylow
134C22×C43—81no—
135C22×C43—81no—
136C22×C43—81no—
137C22×C43—81no—
138C22×C43—81no—
139C22×C43—81no—
140C22×C43#44711yescharacteristic
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—41no—
144C4×C43—41no—
145C4×C43—81no—
146C4×C43—81no—
147C4×C43#44911yescharacteristic
148C4×C43#45311yescharacteristic
149Dic43—161no—
150#3403D4311yescharacteristic
151#2251—431no—
152#2208—431no—
153#1690—431no—
154#1360—431no—
155#1338—431no—
156#1333—431no—
157C2×C43—161no—
158C2×C43—161no—
159C2×C43#162111yescharacteristic
160C2×C43#219111yescharacteristic
161C2×C43#219411yescharacteristic
162#559—21no—
163C2×Q32—861no—
164C2×SD32—861no—
165C2×SD32—861no—
166#496—21no—
167#495C2×D4311yescharacteristic
168#494—431no—
169#475—861no—
170#464—21no—
171#463—21no—
172#459—21no—
173#446C2×D4311yescharacteristic
174#440—21no—
175C4×D8C2×D4311yescharacteristic
176C4⋊C16—431no—
177#358—861no—
178#346—431no—
179#334—431no—
180#332—861no—
181C43#1233811yescharacteristic, complemented, Sylow
182C2×Q16—861no—
183C2×Q16—861no—
184C2×Q16C22⋊D4311yescharacteristic
185C2×SD16—21no—
186C2×SD16—21no—
187C2×D8—21no—
188C2×D8C22⋊D4311yescharacteristic
189C2×D8C22⋊D4311yescharacteristic
190C4⋊Q8—861no—
191#127—21no—
192#124—21no—
193#124—21no—
194#124—41no—
195#123—41no—
196#123—41no—
197C4×Q8—21no—
198C4×Q8C22⋊D4311yescharacteristic
199C4×D4—21no—
200C4×D4—21no—
201C4×D4—41no—
202Q32—1722no—
203SD32—1722no—
204SD32—1722no—
205C2×C16—861no—
206C2×C16—861no—
207#107C22⋊D4311yescharacteristic
208#106—1721no—
209C4⋊C8—21no—
210C4⋊C8—861no—
211C4⋊C8C22⋊D4311yescharacteristic
212#103—21no—
213#103—1721no—
214#102—21no—
215#102—21no—
216#97—21no—
217C4×C8C22×D4311yescharacteristic
218C2×Q8—21no—
219C2×Q8—1721no—
220C2×Q8#1062188211yescharacteristic
221C2×D4—21no—
222C2×D4—21no—
223C2×D4—41no—
224C2×D4—41no—
225C22×C4—41no—
226C22×C4—41no—
227Q16—41no—
228Q16—1721no—
229Q16—1721no—
230Q16—1721no—
231Q16—1721no—
232SD16—41no—
233SD16—41no—
234SD16—81no—
235D8—21no—
236D8—21no—
237D8—41no—
238D8—81no—
239C2×C8—21no—
240C2×C8—1721no—
241C2×C8C2×C22⋊D4311yescharacteristic
242C2×C8C2×C22⋊D4311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—1721no—
247C4⋊C4—1721no—
248C4⋊C4#1062188211yescharacteristic
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C42—21no—
256C42—41no—
257C42C2×C22⋊D4311yescharacteristic
258C16—862no—
259C16—1721no—
260C23—41no—
261C23—41no—
262Q8—41no—
263Q8—41no—
264Q8—41no—
265Q8—3441no—
266Q8—3441no—
267D4—41no—
268D4—41no—
269D4—41no—
270D4—41no—
271D4—82no—
272D4—161no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—161no—
278C2×C4—161no—
279C2×C4—3441no—
280C2×C4#1306329411yescharacteristic
281C2×C4C2×#1062188211yescharacteristic
282C2×C4#1306335111yescharacteristic
283C8—21no—
284C8—41no—
285C8—3441no—
286C8#1306334511yescharacteristic
287C8#1306335011yescharacteristic
288C22—81no—
289C22—81no—
290C22—81no—
291C22—81no—
292C22—81no—
293C22—81no—
294C22#1458303311yescharacteristic
295C4—21no—
296C4—21no—
297C4—41no—
298C4—41no—
299C4—81no—
300C4—81no—
301C4—6881no—
302C4#1458304411yescharacteristic
303C4#1458306711yescharacteristic
304C2—161no—
305C2—161no—
306C2#1913366011yescharacteristic
307C2#1913654611yescharacteristic
308C2#1913656611yescharacteristic
subgroupG/H
centerC22#14583033
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
Fitting, prime radicalC43×#3403C2
socleC22×C43#447
hypercenter#3403D43
hypocenterC43#12338
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #3403

Complements

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

NH ≅ G/Ntype
1. #19136867C2semidirect
2. #19136640C2semidirect
3. #19134089C2semidirect
4. #19132638C2semidirect
5. #19132577C2semidirect
6. #19132562C2semidirect
181. C43#12338semidirect

Maximal subgroups

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

subgroupindex
#191368672
#191366402
#191340892
#191326382
#191325772
#191325622
C43×#34032
#1233843