Finite Group Databasebeta

← #25010062

Subgroups — #25010062

Order 11008.

368 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 71 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
1Q16×D172C211yesmaximal, characteristic
2#19136847C211yesmaximal, characteristic, complemented
3#19133957C211yesmaximal, characteristic
4#19132645C211yesmaximal, characteristic, complemented
5#19132559C211yesmaximal, characteristic, complemented
6#19132549C211yesmaximal, characteristic
7C43×#2209C211yesmaximal, characteristic, complemented
8C2×Q16×D43—21no—
9Q8×D172—21no—
10C2×#13063271—22no—
11#14583279C2211yescharacteristic
12#14583176—21no—
13#14583141—21no—
14#14583109—21no—
15#14583056—22no—
16C8×D172C2211yescharacteristic
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582645—21no—
20C2×Q32×C43—21no—
21C43×#494C2211yescharacteristic
22C4×Q16×C43C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#358—21no—
25C2×Q8×D43—22no—
26C2×Dic172—21no—
27C2×Dic172D412yes—
28C2×#10621885—22no—
29Q16×D43—42no—
30Q16×D43—42no—
31C2×C8×D43—21no—
32#13063325—21no—
33#13063325—41no—
34#13063305—22no—
35#13063305—42no—
36C4×D172—41no—
37C4×D172D411yescharacteristic
38#13063271—44no—
39C2×C43⋊C16—21no—
40#13063258—41no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)D411yescharacteristic
43#13063248—22no—
44#13063245—41no—
45(C2×D43)⋊C8—21no—
46C2×Q16×C43—21no—
47C2×Q16×C43—21no—
48C2×Q16×C43D411yescharacteristic
49C4⋊Q8×C43—21no—
50C4×Q8×C43—21no—
51Q32×C43—42no—
52C2×C16×C43—21no—
53#107×C43D411yescharacteristic
54#103×C43—21no—
55C4×C8×C43C2311yescharacteristic
56C2×Q8×C43—21no—
57C2×Q8×C43—41no—
58Q8×D43—44no—
59Q8×D43—82no—
60C2×D172D811yescharacteristic
61C2×C4×D43—21no—
62C2×C4×D43—42no—
63C2×Dic86—22no—
64C2×Dic86—42no—
65Q16×C43—21no—
66Q16×C43—42no—
67Q16×C43—41no—
68Q16×C43—41no—
69Q16×C43D812yes—
70C2×C8×C43C2×D411yescharacteristic
71C2×C8×C43C2×D411yescharacteristic
72C4⋊C4×C43—21no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C42×C43—41no—
77C42×C43C2×D411yescharacteristic
78#10621885—44no—
79(C2×D43)⋊C4—21no—
80(C2×D43)⋊C4—42no—
81C4⋊Dic43—42no—
82C4⋊Dic43—41no—
83C4⋊Dic43—41no—
84C4⋊Dic43D811yescharacteristic
85C2×C43⋊C8—21no—
86C2×C43⋊C8—41no—
87Dic172—42no—
88Dic172—41no—
89Dic172—41no—
90C8×D43—41no—
91C8×D43—41no—
92C16×C43—41no—
93C43⋊C16—22no—
94C22×D43—21no—
95Q8×C43—22no—
96Q8×C43—41no—
97Q8×C43—81no—
98Q8×C43—81no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—81no—
102C2×C4×C43#12011yescharacteristic
103C2×C4×C43C2×D811yescharacteristic
104C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
105C2×Dic43—21no—
106C2×Dic43—42no—
107D172—21no—
108D172Q3212yescomplemented
109C4×D43—41no—
110C4×D43—41no—
111C4×D43—84no—
112Dic86—42no—
113Dic86—42no—
114Dic86—84no—
115C8×C43—21no—
116C8×C43C2×D811yescharacteristic
117C8×C43AGL(1,ℤ/8)11yescharacteristic
118C43⋊C8—41no—
119C43⋊C8—81no—
120#12322—431nomaximal, Sylow
121C22×C43#44711yescharacteristic
122C2×D43—22no—
123C2×D43—41no—
124C2×D43—41no—
125C4×C43—21no—
126C4×C43—42no—
127C4×C43—81no—
128C4×C43—161no—
129C4×C43#44711yescharacteristic
130C4×C43#45311yescharacteristic
131C4×C43C2×Q3211yescharacteristic
132C4×C43#51011yescharacteristic
133Dic43—41no—
134Dic43—82no—
135D4×Q16—431no—
136#2247—431no—
137#2209D4311yescharacteristic, complemented
138#1669—431no—
139#1362—431no—
140#1332—431no—
141D4⋊C16—431no—
142C2×C43#161911yescharacteristic
143C2×C43#218811yescharacteristic
144C2×C43#219511yescharacteristic
145D43—42no—
146C22×Q16—861no—
147D4×Q8—861no—
148C2×Q32—21no—
149C2×Q32—862no—
150#494—431no—
151#494C2×D4311yescharacteristic
152#474—861no—
153#467—861no—
154#462—861no—
155#451—862no—
156C4×Q16C2×D4311yescharacteristic
157C8×D4—431no—
158C4⋊C16C2×D4311yescharacteristic
159#358—21no—
160C4×C16—431no—
161#335—431no—
162#332—861no—
163C43#1232211yescharacteristic, complemented, Sylow
164C22×Q8—862no—
165C2×Q16—21no—
166C2×Q16—21no—
167C2×Q16—432no—
168C2×Q16—862no—
169C2×Q16—861no—
170C2×Q16—1722no—
171C2×Q16—1722no—
172C2×Q16C22⋊D4311yescharacteristic
173C22×C8—861no—
174C4⋊Q8—21no—
175C4⋊Q8—861no—
176C4⋊Q8—1721no—
177C22⋊Q8—862no—
178C22⋊Q8—1722no—
179C4×Q8—21no—
180C4×D4—431no—
181C4×D4—1721no—
182Q32—42no—
183Q32—1724no—
184C2×C16—21no—
185C2×C16—861no—
186#107—1721no—
187#107C22⋊D4311yescharacteristic
188C4⋊C8—431no—
189C4⋊C8—861no—
190#103—21no—
191#103—862no—
192#102—1721no—
193C22⋊C8—861no—
194C4×C8C22×D4311yescharacteristic
195C2×Q8—21no—
196C2×Q8—41no—
197C2×Q8—862no—
198C2×Q8—3442no—
199C2×Q8—1722no—
200C2×Q8—1724no—
201C2×D4—431no—
202C22×C4—861no—
203C22×C4—1722no—
204Q16—21no—
205Q16—42no—
206Q16—41no—
207Q16—41no—
208Q16—1722no—
209Q16—1724no—
210Q16—1721no—
211Q16—1721no—
212Q16#1062188212yes—
213C2×C8—861no—
214C2×C8—1721no—
215C2×C8—1721no—
216C2×C8—1721no—
217C2×C8D4×D4311yescharacteristic
218C2×C8C2×C22⋊D4311yescharacteristic
219C4⋊C4—21no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—431no—
224C4⋊C4—1722no—
225C4⋊C4—1721no—
226C4⋊C4—1721no—
227C22⋊C4—861no—
228C22⋊C4—1722no—
229C42—41no—
230C42D4×D4311yescharacteristic
231C16—41no—
232C16—862no—
233C23—861no—
234Q8—22no—
235Q8—41no—
236Q8—81no—
237Q8—81no—
238Q8—3444no—
239Q8—1722no—
240Q8—1722no—
241D4—432no—
242D4—861no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—81no—
246C2×C4—861no—
247C2×C4—3444no—
248C2×C4—1722no—
249C2×C4—1721no—
250C2×C4—1721no—
251C2×C4#1306329311yescharacteristic
252C2×C4D8×D4311yescharacteristic
253C2×C4#1306334911yescharacteristic
254C8—21no—
255C8—3441no—
256C8—1721no—
257C8C2×#1062188211yescharacteristic
258C8#1306335011yescharacteristic
259C22—862no—
260C22—1721no—
261C22—1721no—
262C22#1458303111yescharacteristic
263C4—21no—
264C4—42no—
265C4—81no—
266C4—161no—
267C4—3442no—
268C4—1721no—
269C4#1458303211yescharacteristic
270C4#1458306511yescharacteristic
271C4Q32×D4311yescharacteristic
272C4#1458334111yescharacteristic
273C2—1722no—
274C2#1913364811yescharacteristic
275C2#1913652711yescharacteristic
276C2#1913657011yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2209C2
socleC22×C43#447
prime radicalC2×D172D8
hypercenter#2209D43
hypocenterC43#12322
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
2. #19136847C2semidirect
4. #19132645C2semidirect
5. #19132559C2semidirect
7. C43×#2209C2semidirect
108. D172Q32semidirect
137. #2209D43semidirect
163. C43#12322semidirect

Maximal subgroups

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

subgroupindex
Q16×D1722
#191368472
#191339572
#191326452
#191325592
#191325492
C43×#22092
#1232243