Finite Group Databasebeta

← #24990198

Subgroups — #24990198

Order 11008.

426 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 115 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#19134587C211yesmaximal, characteristic
2#19132916C211yesmaximal, characteristic
3#19132498C212yesmaximal, complemented
4#19132453C212yesmaximal, complemented
5C43×#2357C211yesmaximal, characteristic
6#14582952C2212yes—
7#14582923C2212yes—
8C2×#13063242—21no—
9#14582668—21no—
10#14582623—22no—
11C2×C4×D4×C43C2211yescharacteristic
12C43×#390—21no—
13C43×#388—22no—
14C43×#382C2211yescharacteristic
15C43×#381C412yes—
16C4×C4⋊C4×C43—21no—
17C4×C4⋊C4×C43C2211yescharacteristic
18C4×C22⋊C4×C43C412yes—
19C2×#10621877—22no—
20C4⋊(C43⋊C8)—22no—
21C4⋊(C43⋊C8)—22no—
22C4⋊(C43⋊C8)—22no—
23#13063242—42no—
24C22⋊(C43⋊C8)—22no—
25C4×C43⋊C8—22no—
26C22×D4×C43D411yescharacteristic
27C23×C4×C43C2×C412yes—
28C4×D4×C43—22no—
29C4×D4×C43—22no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43D411yescharacteristic
33C2×C22⋊C4×C43—22no—
34C2×C22⋊C4×C43—22no—
35C2×C22⋊C4×C43D412yes—
36C2×C42×C43—21no—
37C2×C42×C43—22no—
38C2×C42×C43C2311yescharacteristic
39#95×C43—22no—
40#95×C43—21no—
41#95×C43C2×C411yescharacteristic
42#95×C43C2×C412yes—
43#95×C43C2×C411yescharacteristic
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—21no—
52C22×C4×C43—22no—
53C22×C4×C43—21no—
54C22×C4×C43—82no—
55C22×C4×C43C22⋊C412yes—
56C22×C4×C43C22×C411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C4⋊C4×C43—22no—
60C4⋊C4×C43—42no—
61C4⋊C4×C43—41no—
62C4⋊C4×C43—41no—
63C22⋊C4×C43—24no—
64C22⋊C4×C43—44no—
65C22⋊C4×C43—82no—
66C42×C43—42no—
67C42×C43—82no—
68C42×C43#4112yes—
69C42×C43#4112yes—
70#10621877—42no—
71#10621877—42no—
72C2×C43⋊C8—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—22no—
84C2×C4×C43—41no—
85C2×C4×C43—41no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—42no—
95C2×C4×C43—82no—
96C2×C4×C43—82no—
97C2×C4×C43#11711yescharacteristic
98C2×C4×C43#11711yescharacteristic
99C2×C4×C43#12312yes—
100C2×C4×C43#12312yes—
101C2×C4×C43#13512yes—
102C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C43#13711yescharacteristic
104C43⋊C8—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—42no—
122C4×C43—81no—
123C4×C43—82no—
124C4×C43#48212yes—
125C4×C43#48512yes—
126#2357D4311yescharacteristic
127#1800—431no—
128#1460—431no—
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#431—432no—
139#423—432no—
140C2×#100—861no—
141#390—21no—
142#388—22no—
143#382C2×D4311yescharacteristic
144#381Dic4312yes—
145C4×C4⋊C4—21no—
146C4×C4⋊C4C2×D4311yescharacteristic
147C4×C22⋊C4Dic4312yes—
148#343—861no—
149#323—862no—
150C43#877111yescharacteristic, complemented, Sylow
151C22×D4C22⋊D4311yescharacteristic
152C23×C4C2×Dic4312yes—
153C2×M16—862no—
154C4×D4—22no—
155C4×D4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4C22⋊D4311yescharacteristic
159C2×C22⋊C4—22no—
160C2×C22⋊C4—22no—
161C2×C22⋊C4C22⋊D4312yes—
162C2×C42—21no—
163C2×C42—22no—
164C2×C42C22×D4311yescharacteristic
165C4⋊C8—862no—
166C4⋊C8—862no—
167C4⋊C8—862no—
168#100—1722no—
169C22⋊C8—862no—
170C4×C8—862no—
171#95—22no—
172#95—21no—
173#95C2×Dic4311yescharacteristic
174#95C2×Dic4312yes—
175#95C2×Dic4311yescharacteristic
176C24C22⋊Dic4312yes—
177C2×D4—22no—
178C2×D4—22no—
179C2×D4—21no—
180C2×D4—21no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—82no—
187C22×C4C22⋊Dic4312yes—
188C22×C4C22×Dic4311yescharacteristic
189C22×C4C2×C22⋊D4311yescharacteristic
190C22×C4C2×C22⋊D4311yescharacteristic
191M16—1722no—
192M16—1722no—
193C2×C8—1722no—
194C2×C8—1722no—
195C4⋊C4—22no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C22⋊C4—24no—
200C22⋊C4—44no—
201C22⋊C4—82no—
202C42—42no—
203C42—82no—
204C42#1062189812yes—
205C42#1062189812yes—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23C2×C22⋊Dic4311yescharacteristic
212D4—42no—
213D4—42no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—82no—
228C2×C4—82no—
229C2×C4#1306328411yescharacteristic
230C2×C4#1306328411yescharacteristic
231C2×C4#1306330812yes—
232C2×C4#1306330812yes—
233C2×C4#1306334512yes—
234C2×C4#1306335011yescharacteristic
235C2×C4#1306335511yescharacteristic
236C8—3442no—
237C8—3442no—
238C22—21no—
239C22—21no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22—82no—
245C22#1458276211yescharacteristic
246C22#1458289511yescharacteristic
247C22#1458290011yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—81no—
254C4—82no—
255C4#1458322312yes—
256C4#1458324012yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#1913469011yescharacteristic
261C2#1913469911yescharacteristic
262C2#1913470611yescharacteristic
subgroupG/H
centerC22#14582762
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2357C2
socleC22×C43#381
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#2357D43
hypocenterC43#8771
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2357

Complements

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

NH ≅ G/Ntype
3. #19132498C2semidirect
4. #19132453C2semidirect
150. C43#8771semidirect

Maximal subgroups

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

subgroupindex
#191345872
#191329162
#191324982
#191324532
C43×#23572
#877143