Finite Group Databasebeta

← #25010465

Subgroups — #25010465

Order 11008.

306 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 65 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#19147609C211yesmaximal, characteristic
2#19136734C211yesmaximal, characteristic, complemented
3#19133986C211yesmaximal, characteristic, complemented
4#19132641C211yesmaximal, characteristic
5#19132575C211yesmaximal, characteristic, complemented
6#19132560C211yesmaximal, characteristic, complemented
7C43×#2240C211yesmaximal, characteristic
8#14583635—21no—
9#14583282—21no—
10#14583112—22no—
11#14583106—21no—
12#14583096—21no—
13C8×Dic86C2211yescharacteristic
14C4×Dic172C2211yescharacteristic
15D8×Dic43—21no—
16#14582726—21no—
17C4⋊(C43⋊C16)C2211yescharacteristic
18#14582702—21no—
19#14582652C2211yescharacteristic
20#14582645—21no—
21C43×#500C2211yescharacteristic
22C43×#493C2211yescharacteristic
23C43×#357—22no—
24C4×C16×C43C2211yescharacteristic
25C2×Dic172D411yescharacteristic
26C2×#10621885—41no—
27C2×#10621883—22no—
28#13063312—22no—
29#13063312—41no—
30#13063306—42no—
31C4×Dic86—21no—
32C4×Dic86D411yescharacteristic
33D4×Dic43—22no—
34D4×Dic43—41no—
35C2×C43⋊C16—21no—
36#13063259D411yescharacteristic
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)D411yescharacteristic
39Dic43⋊C8—21no—
40#13063250—21no—
41#13063249—41no—
42#13063246—22no—
43C8×Dic43—21no—
44C2×D8×C43—21no—
45C2×D8×C43D412yes—
46C4⋊Q8×C43—21no—
47#127×C43—21no—
48C2×C16×C43—21no—
49#107×C43—21no—
50#107×C43—21no—
51C4×C8×C43C2311yescharacteristic
52C2×Q8×C43—41no—
53C2×D4×C43—22no—
54C2×D4×C43—41no—
55C2×D4×C43—41no—
56C22×Dic43—42no—
57C2×Dic86—21no—
58C2×Dic86D811yescharacteristic
59D8×C43—42no—
60D8×C43—41no—
61D8×C43—41no—
62C2×C8×C43C2×D411yescharacteristic
63C2×C8×C43C2×D411yescharacteristic
64C4⋊C4×C43—41no—
65C4⋊C4×C43—41no—
66C42×C43C2×D411yescharacteristic
67C22⋊Dic43—42no—
68C22⋊Dic43—42no—
69C22⋊Dic43—42no—
70#10621885—82no—
71#10621883—82no—
72C4⋊Dic43—21no—
73C4⋊Dic43D811yescharacteristic
74Dic43⋊C4—21no—
75Dic43⋊C4—41no—
76C4×Dic43—21no—
77C4×Dic43—41no—
78C2×C43⋊C8—21no—
79C2×C43⋊C8—41no—
80Dic172—21no—
81Dic172—21no—
82C16×C43—41no—
83C43⋊C16—41no—
84C23×C43—42no—
85Q8×C43—81no—
86Q8×C43—81no—
87D4×C43—42no—
88D4×C43—42no—
89D4×C43—81no—
90D4×C43—81no—
91D4×C43—161no—
92C2×C4×C43—81no—
93C2×C4×C43#12011yescharacteristic
94C2×C4×C43C2×D811yescharacteristic
95C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
96C2×Dic43—21no—
97C2×Dic43—21no—
98C2×Dic43—41no—
99C2×Dic43—41no—
100C2×Dic43—162no—
101Dic86—21no—
102Dic86—21no—
103Dic86—41no—
104Dic86—41no—
105C8×C43—21no—
106C8×C43#13511yescharacteristic
107C8×C43#13711yescharacteristic
108C43⋊C8—41no—
109C43⋊C8—81no—
110#12381—431nomaximal, Sylow
111C22×C43—82no—
112C22×C43—82no—
113C22×C43—82no—
114C22×C43#44711yescharacteristic
115C4×C43—21no—
116C4×C43—161no—
117C4×C43#45211yescharacteristic
118C4×C43#45511yescharacteristic
119C4×C43#50811yescharacteristic
120C4×C43#50911yescharacteristic
121Dic43—41no—
122Dic43—41no—
123Dic43—81no—
124Dic43—81no—
125#3396—431no—
126#2240D4311yescharacteristic
127#2225—431no—
128#1674—431no—
129#1361—431no—
130Q8⋊C16—431no—
131#1332—431no—
132C2×C43—162no—
133C2×C43#164111yescharacteristic
134C2×C43#218611yescharacteristic
135C2×C43#219411yescharacteristic
136#559—861no—
137#500C2×D4311yescharacteristic
138#495—861no—
139#493C2×D4311yescharacteristic
140#463—862no—
141#462—861no—
142#460—861no—
143C8×Q8—431no—
144C4×Q16—431no—
145C4×D8—861no—
146#367—861no—
147C4⋊C16—431no—
148#358—861no—
149#357—22no—
150C4×C16C2×D4311yescharacteristic
151#335—431no—
152#332—861no—
153C43#1238111yescharacteristic, complemented, Sylow
154C2×Q16—431no—
155C2×Q16—1721no—
156C2×SD16—862no—
157C2×D8—21no—
158C2×D8C22⋊D4312yes—
159C4⋊Q8—21no—
160#127—21no—
161#124—862no—
162#124—1721no—
163#123—1722no—
164C4×Q8—431no—
165C4×Q8—861no—
166C4×D4—862no—
167C4×D4—1721no—
168C2×C16—21no—
169C2×C16—861no—
170#107—21no—
171#107—21no—
172#107—431no—
173C4⋊C8—431no—
174C4⋊C8—861no—
175C4⋊C8—861no—
176#103—861no—
177#103—1721no—
178#102—862no—
179C4×C8—861no—
180C4×C8C22×D4311yescharacteristic
181C2×Q8—41no—
182C2×Q8—431no—
183C2×Q8—861no—
184C2×D4—22no—
185C2×D4—41no—
186C2×D4—41no—
187C22×C4—1722no—
188Q16—861no—
189Q16—861no—
190Q16—3442no—
191SD16—3442no—
192D8—42no—
193D8—41no—
194D8—41no—
195C2×C8—861no—
196C2×C8—1721no—
197C2×C8D4×D4311yescharacteristic
198C2×C8C2×C22⋊D4311yescharacteristic
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—431no—
202C4⋊C4—861no—
203C4⋊C4—861no—
204C4⋊C4—1721no—
205C22⋊C4—1722no—
206C22⋊C4—1722no—
207C22⋊C4—1722no—
208C42—861no—
209C42—1721no—
210C42D4×D4311yescharacteristic
211C16—41no—
212C16—1721no—
213C23—42no—
214Q8—81no—
215Q8—81no—
216Q8—861no—
217Q8—861no—
218Q8—1721no—
219Q8—1721no—
220D4—42no—
221D4—42no—
222D4—81no—
223D4—81no—
224D4—161no—
225C2×C4—81no—
226C2×C4—861no—
227C2×C4—861no—
228C2×C4—1721no—
229C2×C4—1721no—
230C2×C4—6882no—
231C2×C4#1306329311yescharacteristic
232C2×C4D8×D4311yescharacteristic
233C2×C4#1306334911yescharacteristic
234C8—21no—
235C8—3441no—
236C8—1721no—
237C8#1306334611yescharacteristic
238C8#1306335411yescharacteristic
239C22—82no—
240C22—82no—
241C22—82no—
242C22#1458303111yescharacteristic
243C4—21no—
244C4—161no—
245C4—3441no—
246C4—3441no—
247C4—1721no—
248C4—1721no—
249C4#1458305811yescharacteristic
250C4#1458307611yescharacteristic
251C4#1458332811yescharacteristic
252C4#1458333311yescharacteristic
253C2—162no—
254C2#1913378511yescharacteristic
255C2#1913651511yescharacteristic
256C2#1913656511yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2240C2
socleC22×C43#447
prime radicalC43×#493C22
hypercenter#2240D43
hypocenterC43#12381
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
2. #19136734C2semidirect
3. #19133986C2semidirect
5. #19132575C2semidirect
6. #19132560C2semidirect
153. C43#12381semidirect

Maximal subgroups

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

subgroupindex
#191476092
#191367342
#191339862
#191326412
#191325752
#191325602
C43×#22402
#1238143