Finite Group Databasebeta

← #25005878

Subgroups — #25005878

Order 11008.

428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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#19137162C211yesmaximal, characteristic
2#19132917C212yesmaximal
3#19132541C211yesmaximal, characteristic
4#19132528C212yesmaximal
5C43×#1325C211yesmaximal, characteristic
6C2×#13063325C411yescharacteristic
7C2×#13063290C411yescharacteristic
8C2×#13063290C2211yescharacteristic
9#14582949—22no—
10#14582804C411yescharacteristic
11#14582804C2211yescharacteristic
12#14582795—22no—
13C4⋊C4×Dic43—22no—
14C42×Dic43C411yescharacteristic
15#14582625C2212yes—
16#14582624—22no—
17C43×#384C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86C2×C411yescharacteristic
20C22×Dic86C2×C411yescharacteristic
21#13063325—22no—
22#13063325C814yescomplemented
23#13063290—41no—
24#13063290—41no—
25#13063290—41no—
26#13063290—41no—
27C2×C4⋊Dic43—22no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4D412yes—
30C2×C4×Dic43—21no—
31C2×C4×Dic43—21no—
32C2×C4×Dic43—21no—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43C2×C411yescharacteristic
35C2×C4×Dic43D412yes—
36Dic43⋊C8—42no—
37C22⋊(C43⋊C8)—22no—
38C8×Dic43—42no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43C2×C411yescharacteristic
43C2×C4⋊C4×C43C2311yescharacteristic
44C2×C42×C43C2×C411yescharacteristic
45C22⋊C8×C43—22no—
46C22×C4×C43—21no—
47C22×C4×C43—21no—
48C22×C4×C43C22×C411yescharacteristic
49C22×C4×C43C2×D412yes—
50C22×Dic43—21no—
51C22×Dic43—21no—
52C22×Dic43C22⋊C412yes—
53C22×Dic43C22⋊C411yescharacteristic
54C22×Dic43C22⋊C411yescharacteristic
55C2×Dic86—21no—
56C2×Dic86—41no—
57C2×Dic86—41no—
58C2×Dic86—41no—
59C2×Dic86—41no—
60C2×Dic86C2×C812yes—
61C2×Dic86C2×C812yes—
62C2×Dic86M1612yes—
63C2×C8×C43—42no—
64C4⋊C4×C43—41no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—44no—
67C42×C43—21no—
68C42×C43C2×C812yes—
69C4⋊Dic43—28no—
70Dic43⋊C4—42no—
71Dic43⋊C4—42no—
72C4×Dic43—24no—
73C4×Dic43—22no—
74C4×Dic43—22no—
75C4×Dic43—21no—
76C4×Dic43—21no—
77C4×Dic43—42no—
78C4×Dic43—41no—
79C4×Dic43—41no—
80C4×Dic43—41no—
81C2×C43⋊C8—42no—
82C23×C43C2×C22⋊C411yescharacteristic
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—21no—
88C2×C4×C43—22no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—41no—
92C2×C4×C43C22×C811yescharacteristic
93C2×C4×C43C2×M1611yescharacteristic
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—21no—
100C2×Dic43—41no—
101C2×Dic43—41no—
102C2×Dic43—41no—
103C2×Dic43—41no—
104C2×Dic43—41no—
105C2×Dic43C22⋊C814yes—
106C2×Dic43#9911yescharacteristic
107C2×Dic43#9911yescharacteristic
108Dic86—42no—
109Dic86—42no—
110Dic86—42no—
111Dic86—42no—
112C8×C43—82no—
113C43⋊C8—82no—
114#11478—431nomaximal, Sylow
115C22×C43—21no—
116C22×C43—21no—
117C22×C43C2×C22⋊C811yescharacteristic
118C22×C43C2×#9911yescharacteristic
119C22×C43#41311yescharacteristic
120C4×C43—24no—
121C4×C43—21no—
122C4×C43—21no—
123C4×C43—42no—
124C4×C43—81no—
125Dic43—21no—
126Dic43—24no—
127Dic43—42no—
128Dic43—41no—
129Dic43—42no—
130Dic43#35612yes—
131C4×C4⋊Q8—431no—
132#1461—432no—
133#1325—431no—
134#1325D4311yescharacteristic
135#1319—432no—
136C2×C43—21no—
137C2×C43—21no—
138C2×C43#145911yescharacteristic
139C2×C43#212611yescharacteristic
140C2×C43C2×#35611yescharacteristic
141C2×C4⋊Q8—431no—
142C2×C4×Q8—431no—
143C2×C4×Q8—431no—
144#431—862no—
145#391—431no—
146#391—431no—
147#389—862no—
148#384C2×D4311yescharacteristic
149C4×C4⋊C4—862no—
150C43—431no—
151#324—432no—
152#324—862no—
153#324C2×D4312yes—
154C43#1147811yescharacteristic, complemented, Sylow
155C22×Q8—431no—
156C22×Q8—431no—
157C4⋊Q8—434no—
158C4⋊Q8—862no—
159C4×Q8—1721no—
160C4×Q8—1721no—
161C4×Q8—1721no—
162C4×Q8—1721no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—432no—
165C2×C4⋊C4—862no—
166C2×C4⋊C4—861no—
167C2×C4⋊C4C4×D4311yescharacteristic
168C2×C4⋊C4C22×D4311yescharacteristic
169C2×C42—431no—
170C2×C42—432no—
171C2×C42—431no—
172C2×C42—861no—
173C2×C42—861no—
174C2×C42—861no—
175C2×C42C4×D4311yescharacteristic
176C4⋊C8—1722no—
177C22⋊C8—22no—
178C22⋊C8—862no—
179C4×C8—1722no—
180#95—862no—
181#95—862no—
182C2×Q8—432no—
183C2×Q8—432no—
184C2×Q8—432no—
185C2×Q8—861no—
186C2×Q8—1721no—
187C2×Q8—1721no—
188C2×Q8—1721no—
189C2×Q8—1721no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—432no—
193C22×C4—431no—
194C22×C4—431no—
195C22×C4—861no—
196C22×C4—861no—
197C22×C4C2×C4×D4311yescharacteristic
198C22×C4D4×D4312yes—
199C2×C8—42no—
200C2×C8—1722no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—44no—
204C4⋊C4—868no—
205C4⋊C4—1722no—
206C4⋊C4—1722no—
207C42—21no—
208C42—862no—
209C42—862no—
210C42—861no—
211C42—861no—
212C42—864no—
213C42—1721no—
214C42—1722no—
215C42—1721no—
216C42—1721no—
217C42C8×D4312yes—
218C23C22⋊C4×D4311yescharacteristic
219Q8—1722no—
220Q8—1722no—
221Q8—1722no—
222Q8—1722no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—431no—
233C2×C4—434no—
234C2×C4—431no—
235C2×C4—862no—
236C2×C4—862no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4—861no—
241C2×C4—1721no—
242C2×C4—1721no—
243C2×C4—1721no—
244C2×C4—1721no—
245C2×C4—1721no—
246C2×C4C2×C8×D4311yescharacteristic
247C2×C4M16×D4311yescharacteristic
248C8—82no—
249C8—3442no—
250C22—21no—
251C22—21no—
252C22C22⋊C8×D4311yescharacteristic
253C22#99×D4311yescharacteristic
254C22#1458288211yescharacteristic
255C4—24no—
256C4—21no—
257C4—21no—
258C4—42no—
259C4—81no—
260C4—432no—
261C4—861no—
262C4—864no—
263C4—1722no—
264C4—1721no—
265C4—1722no—
266C2—21no—
267C2—21no—
268C2#1913291211yescharacteristic
269C2#1913625711yescharacteristic
270C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1325C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1325D43
hypocenterC43#11478
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
22. #13063325C8semidirect
154. C43#11478semidirect

Maximal subgroups

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

subgroupindex
#191371622
#191329172
#191325412
#191325282
C43×#13252
#1147843