Finite Group Databasebeta

← #24990199

Subgroups — #24990199

Order 11008.

426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 107 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#19137568C211yesmaximal, characteristic
2#19134587C211yesmaximal, characteristic
3#19132497C212yesmaximal, complemented
4#19132454C212yesmaximal, complemented
5C43×#1460C211yesmaximal, characteristic
6#14582923C2212yes—
7C2×#13063242—21no—
8#14582802—21no—
9#14582792—22no—
10#14582765C2211yescharacteristic
11#14582762C412yes—
12C4⋊C4×Dic43—21no—
13C4×C4⋊Dic43C2211yescharacteristic
14C4×C22⋊Dic43C412yes—
15#14582668—21no—
16C2×C4×D4×C43C2211yescharacteristic
17C43×#431C2212yes—
18C43×#323—22no—
19C2×#10621877—22no—
20C2×C4⋊Dic43—21no—
21C2×C4⋊Dic43—21no—
22C2×C22⋊Dic43—22no—
23C2×C22⋊Dic43—22no—
24C2×C4×Dic43—21no—
25C2×C4×Dic43—22no—
26C4⋊(C43⋊C8)—22no—
27C4⋊(C43⋊C8)—22no—
28#13063242—42no—
29C43⋊#95—22no—
30C43⋊#95—21no—
31C43⋊#95C2×C411yescharacteristic
32C43⋊#95C2×C412yes—
33C43⋊#95C2×C411yescharacteristic
34C22×D4×C43D411yescharacteristic
35C23×C4×C43C2×C412yes—
36C4×D4×C43—22no—
37C4×D4×C43—22no—
38C2×C4⋊C4×C43D411yescharacteristic
39C2×C22⋊C4×C43D412yes—
40C2×C42×C43C2311yescharacteristic
41C4⋊C8×C43—22no—
42C22⋊C8×C43—22no—
43C4×C8×C43—22no—
44C24×C43C22⋊C412yes—
45C2×D4×C43—22no—
46C2×D4×C43—22no—
47C2×D4×C43—21no—
48C2×D4×C43—21no—
49C22×C4×C43—22no—
50C22×C4×C43—22no—
51C22×C4×C43—82no—
52C22×C4×C43C22⋊C412yes—
53C22×C4×C43C22×C411yescharacteristic
54C22×C4×C43C2×D411yescharacteristic
55C22×C4×C43C2×D411yescharacteristic
56C22×Dic43—21no—
57C22×Dic43—22no—
58C22×Dic43—21no—
59C2×C8×C43—42no—
60C4⋊C4×C43—22no—
61C22⋊C4×C43—24no—
62C42×C43#4112yes—
63C42×C43#4112yes—
64C22⋊Dic43—44no—
65C22⋊Dic43—82no—
66C4⋊Dic43—42no—
67C4⋊Dic43—41no—
68C4⋊Dic43—41no—
69C4×Dic43—42no—
70C4×Dic43—82no—
71#10621877—42no—
72#10621877—42no—
73C2×C43⋊C8—42no—
74C23×C43—22no—
75C23×C43—22no—
76C23×C43—22no—
77C23×C43—42no—
78C23×C43—42no—
79C23×C43C2×C22⋊C411yescharacteristic
80D4×C43—42no—
81D4×C43—42no—
82C2×C4×C43—22no—
83C2×C4×C43—41no—
84C2×C4×C43—41no—
85C2×C4×C43—42no—
86C2×C4×C43—82no—
87C2×C4×C43—82no—
88C2×C4×C43#11711yescharacteristic
89C2×C4×C43#11711yescharacteristic
90C2×C4×C43#12312yes—
91C2×C4×C43#12312yes—
92C2×C4×C43#13512yes—
93C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
94C2×C4×C43#13711yescharacteristic
95C2×Dic43—22no—
96C2×Dic43—41no—
97C2×Dic43—41no—
98C2×Dic43—42no—
99C2×Dic43—41no—
100C2×Dic43—42no—
101C2×Dic43—41no—
102C2×Dic43—41no—
103C2×Dic43—42no—
104C8×C43—82no—
105C43⋊C8—82no—
106#8771—431nomaximal, Sylow
107C22×C43—21no—
108C22×C43—21no—
109C22×C43—42no—
110C22×C43—42no—
111C22×C43—42no—
112C22×C43—82no—
113C22×C43—82no—
114C22×C43#38111yescharacteristic
115C22×C43#41611yescharacteristic
116C22×C43#41711yescharacteristic
117C4×C43—22no—
118C4×C43—21no—
119C4×C43—21no—
120C4×C43—42no—
121C4×C43#48212yes—
122C4×C43#48512yes—
123Dic43—42no—
124Dic43—81no—
125Dic43—82no—
126#2357—431no—
127#1800—431no—
128#1460D4311yescharacteristic
129#1303—432no—
130#1286—432no—
131C2×C43—21no—
132C2×C43—21no—
133C2×C43—82no—
134C2×C43#182511yescharacteristic
135C2×C43#182711yescharacteristic
136C2×C43#182911yescharacteristic
137C2×C4×D4C2×D4311yescharacteristic
138#431C2×D4312yes—
139#423—432no—
140C2×#100—861no—
141#390—861no—
142#388—862no—
143#382—431no—
144#381—432no—
145C4×C4⋊C4—431no—
146C4×C4⋊C4—861no—
147C4×C22⋊C4—432no—
148#343—861no—
149#323—22no—
150C43#877111yescharacteristic, complemented, Sylow
151C22×D4D17211yescharacteristic
152C23×C4C4×D4312yes—
153C2×M16—862no—
154C4×D4—22no—
155C4×D4—22no—
156C2×C4⋊C4—861no—
157C2×C4⋊C4—861no—
158C2×C4⋊C4D17211yescharacteristic
159C2×C22⋊C4—862no—
160C2×C22⋊C4—862no—
161C2×C22⋊C4C22⋊D4312yes—
162C2×C42—862no—
163C2×C42—861no—
164C2×C42C22×D4311yescharacteristic
165C4⋊C8—22no—
166C4⋊C8—862no—
167C4⋊C8—862no—
168#100—1722no—
169C22⋊C8—22no—
170C4×C8—22no—
171#95—431no—
172#95—432no—
173#95—431no—
174#95—862no—
175#95—861no—
176C24(C2×D43)⋊C412yes—
177C2×D4—22no—
178C2×D4—22no—
179C2×D4—21no—
180C2×D4—21no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—82no—
184C22×C4—861no—
185C22×C4—862no—
186C22×C4—861no—
187C22×C4(C2×D43)⋊C412yes—
188C22×C4C2×C4×D4311yescharacteristic
189C22×C4C2×D17211yescharacteristic
190C22×C4C2×C22⋊D4311yescharacteristic
191M16—1722no—
192M16—1722no—
193C2×C8—42no—
194C2×C8—1722no—
195C4⋊C4—22no—
196C4⋊C4—1722no—
197C4⋊C4—1721no—
198C4⋊C4—1721no—
199C22⋊C4—24no—
200C22⋊C4—3442no—
201C22⋊C4—1724no—
202C42—3442no—
203C42—1722no—
204C42#1062190012yes—
205C42#1062190012yes—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23C2×(C2×D43)⋊C411yescharacteristic
212D4—42no—
213D4—42no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—82no—
219C2×C4—82no—
220C2×C4—862no—
221C2×C4—1722no—
222C2×C4—1721no—
223C2×C4—1722no—
224C2×C4—1721no—
225C2×C4—1721no—
226C2×C4—1722no—
227C2×C4—1721no—
228C2×C4—1721no—
229C2×C4#1306328111yescharacteristic
230C2×C4#1306328111yescharacteristic
231C2×C4#1306330612yes—
232C2×C4#1306330912yes—
233C2×C4#1306334712yes—
234C2×C4#1306335311yescharacteristic
235C2×C4#1306335811yescharacteristic
236C8—82no—
237C8—3442no—
238C22—21no—
239C22—21no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22—82no—
245C22#1458276011yescharacteristic
246C22#1458289611yescharacteristic
247C22#1458290111yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—3442no—
253C4—3441no—
254C4—1722no—
255C4#1458322412yes—
256C4#1458324112yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#1913469111yescharacteristic
261C2#1913469611yescharacteristic
262C2#1913470411yescharacteristic
subgroupG/H
centerC22#14582760
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1460C2
socleC22×C43#381
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#1460D43
hypocenterC43#8771
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #19132497C2semidirect
4. #19132454C2semidirect
150. C43#8771semidirect

Maximal subgroups

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

subgroupindex
#191375682
#191345872
#191324972
#191324542
C43×#14602
#877143