Finite Group Databasebeta

← #25010472

Subgroups — #25010472

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#19147599C211yesmaximal, characteristic
2#19136734C211yesmaximal, characteristic
3#19133986C211yesmaximal, characteristic
4#19132644C211yesmaximal, characteristic
5#19132575C211yesmaximal, characteristic
6#19132560C211yesmaximal, characteristic
7C43×#2241C211yesmaximal, characteristic
8#14583624—21no—
9#14583277—21no—
10#14583107—22no—
11#14583106—21no—
12#14583106—21no—
13C8×Dic86C2211yescharacteristic
14C4×Dic172C2211yescharacteristic
15Q16×Dic43—21no—
16#14582726—21no—
17C4⋊(C43⋊C16)C2211yescharacteristic
18#14582702—21no—
19#14582652C2211yescharacteristic
20#14582645—21no—
21C43×#500C2211yescharacteristic
22C43×#494C2211yescharacteristic
23C43×#358—22no—
24C4×C16×C43C2211yescharacteristic
25C2×Dic172D411yescharacteristic
26C2×#10621885—22no—
27C2×#10621885—41no—
28#13063323—22no—
29#13063316—41no—
30#13063315—42no—
31Q8×Dic43—22no—
32C4×Dic86—21no—
33C4×Dic86D411yescharacteristic
34#13063290—41no—
35C2×C43⋊C16—21no—
36#13063259D411yescharacteristic
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)D411yescharacteristic
39Dic43⋊C8—21no—
40#13063250—21no—
41#13063249—22no—
42#13063249—41no—
43C8×Dic43—21no—
44C2×Q16×C43—21no—
45C2×Q16×C43D412yes—
46C4⋊Q8×C43—21no—
47C4⋊Q8×C43—21no—
48C2×C16×C43—21no—
49#107×C43—21no—
50#107×C43—21no—
51C4×C8×C43C2311yescharacteristic
52C2×Q8×C43—22no—
53C2×Q8×C43—41no—
54C2×Dic86—21no—
55C2×Dic86D811yescharacteristic
56Q16×C43—42no—
57Q16×C43—41no—
58Q16×C43—41no—
59C2×C8×C43C2×D411yescharacteristic
60C2×C8×C43C2×D411yescharacteristic
61C4⋊C4×C43—41no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—41no—
64C4⋊C4×C43—41no—
65C42×C43C2×D411yescharacteristic
66#10621885—82no—
67#10621885—82no—
68C4⋊Dic43—21no—
69C4⋊Dic43—42no—
70C4⋊Dic43D811yescharacteristic
71Dic43⋊C4—21no—
72Dic43⋊C4—42no—
73Dic43⋊C4—42no—
74Dic43⋊C4—41no—
75C4×Dic43—21no—
76C4×Dic43—42no—
77C4×Dic43—41no—
78C2×C43⋊C8—21no—
79C2×C43⋊C8—41no—
80Dic172—21no—
81Dic172—21no—
82C16×C43—41no—
83C43⋊C16—41no—
84Q8×C43—42no—
85Q8×C43—42no—
86Q8×C43—81no—
87Q8×C43—81no—
88C2×C4×C43—42no—
89C2×C4×C43—81no—
90C2×C4×C43#12011yescharacteristic
91C2×C4×C43C2×D811yescharacteristic
92C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
93C2×Dic43—21no—
94C2×Dic43—21no—
95C2×Dic43—41no—
96C2×Dic43—41no—
97Dic86—21no—
98Dic86—41no—
99Dic86—41no—
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—82no—
110C4×C43—161no—
111C4×C43#45211yescharacteristic
112C4×C43#45511yescharacteristic
113C4×C43C2×SD3211yescharacteristic
114C4×C43#51011yescharacteristic
115Dic43—22no—
116Dic43—41no—
117Dic43—81no—
118Dic43—81no—
119#3395—431no—
120#2241D4311yescharacteristic
121#2225—431no—
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—861no—
132#494C2×D4311yescharacteristic
133#462—861no—
134#462—862no—
135#462—861no—
136C8×Q8—431no—
137C4×Q16—431no—
138C4×Q16—861no—
139#367—861no—
140C4⋊C16—431no—
141#358—22no—
142#358—861no—
143C4×C16C2×D4311yescharacteristic
144#335—431no—
145#332—861no—
146C43#1238211yescharacteristic, complemented, Sylow
147C2×Q16—21no—
148C2×Q16—431no—
149C2×Q16—862no—
150C2×Q16—1721no—
151C2×Q16C22⋊D4312yes—
152C4⋊Q8—21no—
153C4⋊Q8—21no—
154C4⋊Q8—862no—
155#125—1721no—
156#125—1722no—
157C4×Q8—431no—
158C4×Q8—862no—
159C4×Q8—861no—
160C4×Q8—1721no—
161C2×C16—21no—
162C2×C16—861no—
163#107—21no—
164#107—21no—
165#107—431no—
166C4⋊C8—431no—
167C4⋊C8—861no—
168C4⋊C8—861no—
169#103—862no—
170#103—861no—
171#103—1721no—
172C4×C8—861no—
173C4×C8C22×D4311yescharacteristic
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—431no—
177C2×Q8—861no—
178Q16—42no—
179Q16—41no—
180Q16—41no—
181Q16—861no—
182Q16—861no—
183Q16—3442no—
184Q16—3442no—
185C2×C8—861no—
186C2×C8—1721no—
187C2×C8D4×D4311yescharacteristic
188C2×C8C2×C22⋊D4311yescharacteristic
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—431no—
194C4⋊C4—861no—
195C4⋊C4—861no—
196C4⋊C4—1722no—
197C4⋊C4—1722no—
198C4⋊C4—1722no—
199C4⋊C4—1721no—
200C42—861no—
201C42—1722no—
202C42—1721no—
203C42D4×D4311yescharacteristic
204C16—41no—
205C16—1721no—
206Q8—42no—
207Q8—42no—
208Q8—81no—
209Q8—81no—
210Q8—432no—
211Q8—861no—
212Q8—1721no—
213Q8—1721no—
214C2×C4—42no—
215C2×C4—81no—
216C2×C4—861no—
217C2×C4—861no—
218C2×C4—1721no—
219C2×C4—1721no—
220C2×C4#1306329311yescharacteristic
221C2×C4D8×D4311yescharacteristic
222C2×C4#1306334911yescharacteristic
223C8—21no—
224C8—3441no—
225C8—1721no—
226C8#1306334611yescharacteristic
227C8#1306335411yescharacteristic
228C22#1458303111yescharacteristic
229C4—21no—
230C4—82no—
231C4—161no—
232C4—862no—
233C4—3441no—
234C4—3441no—
235C4—1721no—
236C4#1458305811yescharacteristic
237C4#1458307611yescharacteristic
238C4SD32×D4311yescharacteristic
239C4#1458333811yescharacteristic
240C2#1913378511yescharacteristic
241C2#1913651011yescharacteristic
242C2#1913657211yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2241C2
socle, prime radicalC22×C43#447
hypercenter#2241D43
hypocenterC43#12382
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

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
#191475992
#191367342
#191339862
#191326442
#191325752
#191325602
C43×#22412
#1238243