Finite Group Databasebeta

← #25005824

Subgroups — #25005824

Order 11008.

438 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#14582964C211yesmaximal, characteristic
2#19136204C212yesmaximal, complemented
3#19132535C211yesmaximal, characteristic, complemented
4#19132518C212yesmaximal, complemented
5C43×#1322C211yesmaximal, characteristic, complemented
6C22×C8×D43C411yescharacteristic
7C22×C8×D43C2211yescharacteristic
8C2×C4×D172C411yescharacteristic
9C2×#13063264—22no—
10#14582964—22no—
11#14582964—22no—
12C2×(C2×D43)⋊C8C411yescharacteristic
13C2×(C2×D43)⋊C8C2211yescharacteristic
14C2×C4×C43⋊C8C411yescharacteristic
15C22⋊(C43⋊C16)C2212yes—
16(C2×D43)⋊C16—22no—
17C2×C4⋊C8×C43C2211yescharacteristic
18C43×C22⋊C16C2212yes—
19C22×D172C811yescharacteristic
20C22×C4×D43C2×C411yescharacteristic
21C22×C4×D43C2×C411yescharacteristic
22C22×C43⋊C8C2×C411yescharacteristic
23C22×C43⋊C8C2×C411yescharacteristic
24C2×C8×D43—21no—
25C2×C8×D43—21no—
26C2×C8×D43—42no—
27C2×C8×D43—42no—
28C2×C8×D43D412yes—
29C2×C8×D43D412yes—
30C4×D172—22no—
31C4×D172—22no—
32C2×C4⋊Dic43C811yescharacteristic
33C2×(C2×D43)⋊C4C811yescharacteristic
34C2×(C2×D43)⋊C4C811yescharacteristic
35#13063264—44no—
36C2×C43⋊C16—22no—
37(C2×D43)⋊C8—22no—
38(C2×D43)⋊C8—22no—
39C4×C43⋊C8—21no—
40C4×C43⋊C8—21no—
41C22×C8×C43C2×C411yescharacteristic
42C22×C8×C43C2311yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C2×C16×C43—22no—
45C4⋊C8×C43—22no—
46C23×D43C2×C811yescharacteristic
47C23×D43C2×C811yescharacteristic
48C22×C4×C43C2×C811yescharacteristic
49C22×C4×C43C2×C811yescharacteristic
50C22×C4×C43C22×C411yescharacteristic
51C22×Dic43C2×C811yescharacteristic
52C22×Dic43C2×C811yescharacteristic
53C2×D172—22no—
54C2×D172—22no—
55C2×D172—22no—
56C2×C4×D43—21no—
57C2×C4×D43—21no—
58C2×C4×D43—41no—
59C2×C4×D43—41no—
60C2×C4×D43—41no—
61C2×C4×D43—41no—
62C2×C4×D43C22⋊C412yes—
63C2×C4×D43M1612yes—
64C2×C8×C43—21no—
65C2×C8×C43—41no—
66C2×C8×C43—41no—
67C2×C8×C43C2×D412yes—
68C42×C43—21no—
69C42×C43—21no—
70(C2×D43)⋊C4—22no—
71(C2×D43)⋊C4—22no—
72C4⋊Dic43—22no—
73C2×C43⋊C8—22no—
74C2×C43⋊C8—21no—
75C2×C43⋊C8—41no—
76C2×C43⋊C8C22⋊C411yescharacteristic
77C2×C43⋊C8C22⋊C411yescharacteristic
78C8×D43—24no—
79C8×D43—42no—
80C8×D43—42no—
81C8×D43—42no—
82C16×C43—42no—
83C43⋊C16—42no—
84C23×C43C22×C811yescharacteristic
85C22×D43—21no—
86C22×D43—21no—
87C22×D43—21no—
88C22×D43—21no—
89C22×D43—41no—
90C22×D43—41no—
91C22×D43—41no—
92C22×D43—41no—
93C22×D43C22⋊C812yes—
94C22×D43M3212yescomplemented
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—41no—
101C2×C4×C43M3212yescomplemented
102C2×C4×C43C2×C22⋊C411yescharacteristic
103C2×C4×C43C2×M1611yescharacteristic
104C2×Dic43—21no—
105C2×Dic43—41no—
106C2×Dic43—41no—
107C2×Dic43C22⋊C812yes—
108D172—28no—
109C4×D43—22no—
110C4×D43—22no—
111C4×D43—42no—
112C4×D43—42no—
113C4×D43—41no—
114C4×D43—41no—
115C8×C43—22no—
116C8×C43—41no—
117C43⋊C8—21no—
118C43⋊C8—41no—
119C43⋊C8#9912yes—
120#11466—431nomaximal, Sylow
121C22×C43—21no—
122C22×C43—21no—
123C22×C43C2×C22⋊C811yescharacteristic
124C22×C43C2×M3211yescharacteristic
125C22×C43C2×M3211yescharacteristic
126C2×D43—22no—
127C2×D43—22no—
128C2×D43—22no—
129C2×D43—22no—
130C2×D43—42no—
131C2×D43—42no—
132C2×D43—42no—
133C2×D43—41no—
134C2×D43—41no—
135C2×D43—42no—
136C4×C43—22no—
137C4×C43—21no—
138C4×C43—41no—
139C4×C43C2×#9911yescharacteristic
140C4×C43#41311yescharacteristic
141Dic43—22no—
142Dic43—41no—
143C2×C8×D4—431no—
144#2112—432no—
145#1322—431no—
146#1322D4311yescharacteristic, complemented
147#1314—432no—
148C2×C43—21no—
149C2×C43—21no—
150C2×C43#145911yescharacteristic
151C2×C43#211211yescharacteristic
152C2×C43#211511yescharacteristic
153D43—42no—
154D43—42no—
155C23×C8—431no—
156C23×C8—431no—
157C2×C4×D4—431no—
158C2×M32—862no—
159C8×D4—862no—
160C8×D4—862no—
161C2×C4⋊C8C2×D4311yescharacteristic
162C2×C22⋊C8—431no—
163C2×C22⋊C8—431no—
164C2×C4×C8—431no—
165C22⋊C16—432no—
166C22⋊C16—862no—
167C22⋊C16C2×D4312yes—
168C43#1146611yescharacteristic, complemented, Sylow
169C22×D4—431no—
170C23×C4—431no—
171C23×C4—431no—
172C22×C8—431no—
173C22×C8—432no—
174C22×C8—432no—
175C22×C8—431no—
176C22×C8—861no—
177C22×C8—861no—
178C22×C8—1722no—
179C22×C8—1722no—
180C22×C8C4×D4311yescharacteristic
181C22×C8C22×D4311yescharacteristic
182C4×D4—862no—
183C4×D4—862no—
184C2×C4⋊C4—431no—
185C2×C22⋊C4—431no—
186C2×C22⋊C4—431no—
187C2×C42C4×D4311yescharacteristic
188M32—1724no—
189C2×C16—22no—
190C2×C16—862no—
191C4⋊C8—22no—
192C22⋊C8—862no—
193C22⋊C8—862no—
194C4×C8—861no—
195C4×C8—861no—
196C24—431no—
197C24—431no—
198C2×D4—862no—
199C2×D4—862no—
200C2×D4—862no—
201C22×C4—431no—
202C22×C4—432no—
203C22×C4—432no—
204C22×C4—431no—
205C22×C4—861no—
206C22×C4—861no—
207C22×C4—1721no—
208C22×C4—1721no—
209C22×C4—1721no—
210C22×C4—1721no—
211C22×C4C8×D4311yescharacteristic
212C22×C4C8×D4311yescharacteristic
213C22×C4C2×C4×D4311yescharacteristic
214C2×C8—21no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—431no—
218C2×C8—431no—
219C2×C8—864no—
220C2×C8—862no—
221C2×C8—861no—
222C2×C8—1722no—
223C2×C8—1722no—
224C2×C8—1722no—
225C2×C8—1721no—
226C2×C8D4×D4312yes—
227C4⋊C4—862no—
228C22⋊C4—862no—
229C22⋊C4—862no—
230C42—21no—
231C42—21no—
232C16—42no—
233C16—1722no—
234C23—432no—
235C23—432no—
236C23—861no—
237C23—861no—
238C23—861no—
239C23—861no—
240C23—1721no—
241C23—1721no—
242C23—1721no—
243C23—1721no—
244C23C2×C8×D4311yescharacteristic
245D4—868no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—432no—
253C2×C4—862no—
254C2×C4—862no—
255C2×C4—861no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1721no—
259C2×C4—1721no—
260C2×C4—1721no—
261C2×C4—1721no—
262C2×C4#1306326412yescomplemented
263C2×C4C22⋊C4×D4311yescharacteristic
264C2×C4M16×D4311yescharacteristic
265C8—22no—
266C8—41no—
267C8—432no—
268C8—861no—
269C8—1721no—
270C22—21no—
271C22—21no—
272C22—862no—
273C22—862no—
274C22—862no—
275C22—862no—
276C22—1722no—
277C22—1722no—
278C22—1722no—
279C22—1722no—
280C22—1721no—
281C22—1721no—
282C22C22⋊C8×D4311yescharacteristic
283C22M32×D4311yescharacteristic
284C22C2×#1306326411yescharacteristic
285C4—22no—
286C4—21no—
287C4—41no—
288C4—862no—
289C4—1721no—
290C4#99×D4311yescharacteristic
291C4#1458288211yescharacteristic
292C2—21no—
293C2—21no—
294C2—1722no—
295C2—1722no—
296C2#1913291211yescharacteristic
297C2#1913620411yescharacteristic
298C2#1913621411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#1322C2
socleC22×C43C2×C22⋊C8
prime radicalC22×D172C8
cosocleC22×C8×C43C23
hypercenter#1322D43
hypocenterC43#11466
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. #19136204C2semidirect
3. #19132535C2semidirect
4. #19132518C2semidirect
5. C43×#1322C2semidirect
94. C22×D43M32semidirect
101. C2×C4×C43M32semidirect
146. #1322D43semidirect
168. C43#11466semidirect
262. C2×C4#13063264semidirect

Maximal subgroups

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

subgroupindex
C2×#145829642
#191362042
#191325352
#191325182
C43×#13222
#1146643