Finite Group Databasebeta

← #25010474

Subgroups — #25010474

Order 11008.

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

normal subgroups only

This group has 288 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#19147600C211yesmaximal, characteristic
2#19136824C211yesmaximal, characteristic
3#19133986C211yesmaximal, characteristic
4#19132645C211yesmaximal, characteristic
5#19132573C211yesmaximal, characteristic
6#19132559C211yesmaximal, characteristic
7C43×#2225C211yesmaximal, characteristic
8#14583627—21no—
9#14583279C2211yescharacteristic
10#14583277—21no—
11#14583109—21no—
12#14583108—22no—
13#14583106—21no—
14C8×Dic86C2211yescharacteristic
15#14582993—21no—
16#14582702—22no—
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582645—21no—
20C43×#500C2211yescharacteristic
21C4×Q16×C43C2211yescharacteristic
22C43×#367—21no—
23C43×C4⋊C16C2211yescharacteristic
24C43×#358—21no—
25C2×Dic172—21no—
26C2×Dic172D412yes—
27C2×#10621885—22no—
28C2×#10621885—41no—
29#13063325—21no—
30#13063323—22no—
31#13063317—41no—
32#13063315—42no—
33C4×Dic86—41no—
34C4×Dic86D411yescharacteristic
35#13063290—22no—
36C2×C43⋊C16—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)D411yescharacteristic
39Dic43⋊C8—21no—
40#13063249—41no—
41#13063248—22no—
42C8×Dic43—21no—
43C2×Q16×C43D411yescharacteristic
44C4⋊Q8×C43—21no—
45C4×Q8×C43—21no—
46C2×C16×C43—21no—
47#107×C43—21no—
48#107×C43—21no—
49#107×C43D411yescharacteristic
50#103×C43—21no—
51C4×C8×C43C2311yescharacteristic
52C2×Q8×C43—21no—
53C2×Q8×C43—41no—
54C2×Dic86—22no—
55C2×Dic86D811yescharacteristic
56Q16×C43—21no—
57Q16×C43—21no—
58C2×C8×C43C2×D411yescharacteristic
59C2×C8×C43C2×D411yescharacteristic
60C4⋊C4×C43—21no—
61C4⋊C4×C43—41no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—41no—
64C42×C43—41no—
65C42×C43C2×D411yescharacteristic
66#10621885—82no—
67#10621885—82no—
68C4⋊Dic43—41no—
69C4⋊Dic43—41no—
70C4⋊Dic43D811yescharacteristic
71Dic43⋊C4—21no—
72Dic43⋊C4—42no—
73Dic43⋊C4—42no—
74Dic43⋊C4—42no—
75C4×Dic43—21no—
76C4×Dic43—42no—
77C2×C43⋊C8—21no—
78C2×C43⋊C8—41no—
79Dic172—42no—
80Dic172—41no—
81Dic172—41no—
82C16×C43—41no—
83C43⋊C16—41no—
84Q8×C43—41no—
85Q8×C43—41no—
86Q8×C43—81no—
87Q8×C43—81no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—81no—
91C2×C4×C43#12011yescharacteristic
92C2×C4×C43C2×D811yescharacteristic
93C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
94C2×Dic43—21no—
95C2×Dic43—21no—
96C2×Dic43—42no—
97Dic86—21no—
98Dic86—42no—
99Dic86—42no—
100Dic86SD3212yes—
101C8×C43—21no—
102C8×C43#13511yescharacteristic
103C8×C43#13711yescharacteristic
104C43⋊C8—41no—
105C43⋊C8—81no—
106#12382—431nomaximal, Sylow
107C22×C43#44711yescharacteristic
108C4×C43—21no—
109C4×C43—81no—
110C4×C43—81no—
111C4×C43—161no—
112C4×C43#45211yescharacteristic
113C4×C43#45511yescharacteristic
114C4×C43C2×SD3211yescharacteristic
115C4×C43#51011yescharacteristic
116Dic43—22no—
117Dic43—41no—
118Dic43—82no—
119#3395—431no—
120#2241—431no—
121#2225D4311yescharacteristic
122#1674—431no—
123#1362—431no—
124Q8⋊C16—431no—
125#1332—431no—
126C2×C43#164111yescharacteristic
127C2×C43#218511yescharacteristic
128C2×C43#219511yescharacteristic
129#557—861no—
130#500C2×D4311yescharacteristic
131#494—431no—
132#494—861no—
133#462—862no—
134#462—861no—
135#462—861no—
136C8×Q8—431no—
137C4×Q16—861no—
138C4×Q16C2×D4311yescharacteristic
139#367—21no—
140C4⋊C16C2×D4311yescharacteristic
141#358—21no—
142#358—862no—
143C4×C16—431no—
144#335—431no—
145#332—861no—
146C43#1238211yescharacteristic, complemented, Sylow
147C2×Q16—432no—
148C2×Q16—862no—
149C2×Q16—861no—
150C2×Q16—1721no—
151C2×Q16C22⋊D4311yescharacteristic
152C4⋊Q8—21no—
153C4⋊Q8—862no—
154C4⋊Q8—861no—
155#125—1721no—
156#125—1722no—
157C4×Q8—21no—
158C4×Q8—431no—
159C4×Q8—862no—
160C4×Q8—1721no—
161C2×C16—21no—
162C2×C16—861no—
163#107—21no—
164#107—21no—
165#107C22⋊D4311yescharacteristic
166C4⋊C8—431no—
167C4⋊C8—861no—
168C4⋊C8—861no—
169#103—21no—
170#103—862no—
171#103—1721no—
172C4×C8—861no—
173C4×C8C22×D4311yescharacteristic
174C2×Q8—21no—
175C2×Q8—41no—
176C2×Q8—431no—
177C2×Q8—862no—
178Q16—21no—
179Q16—21no—
180Q16—3442no—
181Q16—3442no—
182Q16—1722no—
183Q16—1721no—
184Q16—1721no—
185C2×C8—861no—
186C2×C8—1721no—
187C2×C8D4×D4311yescharacteristic
188C2×C8C2×C22⋊D4311yescharacteristic
189C4⋊C4—21no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—431no—
194C4⋊C4—861no—
195C4⋊C4—1722no—
196C4⋊C4—1722no—
197C4⋊C4—1722no—
198C4⋊C4—1721no—
199C4⋊C4—1721no—
200C42—41no—
201C42—861no—
202C42—1722no—
203C42D4×D4311yescharacteristic
204C16—41no—
205C16—1721no—
206Q8—41no—
207Q8—41no—
208Q8—81no—
209Q8—81no—
210Q8—432no—
211Q8—861no—
212Q8—1722no—
213Q8—1722no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—81no—
217C2×C4—861no—
218C2×C4—861no—
219C2×C4—1722no—
220C2×C4#1306329311yescharacteristic
221C2×C4D8×D4311yescharacteristic
222C2×C4#1306334911yescharacteristic
223C8—21no—
224C8—3441no—
225C8—1721no—
226C8#1306334511yescharacteristic
227C8#1306335611yescharacteristic
228C22#1458303111yescharacteristic
229C4—21no—
230C4—81no—
231C4—81no—
232C4—161no—
233C4—862no—
234C4—3442no—
235C4—1721no—
236C4#1458305911yescharacteristic
237C4#1458307511yescharacteristic
238C4SD32×D4311yescharacteristic
239C4#1458333811yescharacteristic
240C2#1913378711yescharacteristic
241C2#1913651011yescharacteristic
242C2#1913657011yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2225C2
socle, prime radicalC22×C43#447
hypercenter#2225D43
hypocenterC43#12382
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
146. C43#12382semidirect

Maximal subgroups

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

subgroupindex
#191476002
#191368242
#191339862
#191326452
#191325732
#191325592
C43×#22252
#1238243