Finite Group Databasebeta

← #24984723

Subgroups — #24984723

Order 11008.

440 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 111 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#19137164C211yesmaximal, characteristic
2#19134737C212yesmaximal
3#19132421C211yesmaximal, characteristic
4#19132420C212yesmaximal
5C43×#1272C211yesmaximal, characteristic
6C2×#13063323C411yescharacteristic
7C2×Q8×Dic43C411yescharacteristic
8C2×#13063290C411yescharacteristic
9#14582805C2211yescharacteristic
10#14582796—22no—
11#14582768C411yescharacteristic
12#14582750—22no—
13C42×Dic43C2211yescharacteristic
14#14582654C2212yes—
15#14582653—22no—
16#14582653—22no—
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86C2×C411yescharacteristic
20C22×C43⋊C8—22no—
21#13063323—22no—
22#13063323C814yescomplemented
23Q8×Dic43—42no—
24#13063290—42no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—22no—
30C2×C4×Dic43—21no—
31C2×C4×Dic43—21no—
32C2×C4×Dic43C2×C411yescharacteristic
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43D412yes—
35C2×C4×Dic43D412yes—
36C43⋊#95—22no—
37C22×Q8×C43C2×C411yescharacteristic
38C22×C8×C43—22no—
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C42×C43C2311yescharacteristic
41#95×C43—22no—
42C2×Q8×C43—21no—
43C2×Q8×C43—41no—
44C2×Q8×C43—41no—
45C2×Q8×C43C2×C812yes—
46C22×C4×C43—21no—
47C22×C4×C43—21no—
48C22×C4×C43C22×C411yescharacteristic
49C22×C4×C43C2×D412yes—
50C22×Dic43—21no—
51C22×Dic43—21no—
52C22×Dic43C22⋊C411yescharacteristic
53C22×Dic43C22⋊C412yes—
54C22×Dic43C22⋊C411yescharacteristic
55C2×Dic86—21no—
56C2×Dic86—41no—
57C2×Dic86—41no—
58C2×Dic86C2×C812yes—
59C2×C8×C43—42no—
60C2×C8×C43—42no—
61C2×C8×C43—42no—
62C4⋊C4×C43—41no—
63C42×C43—41no—
64C4⋊Dic43—42no—
65C4⋊Dic43—41no—
66Dic43⋊C4—28no—
67Dic43⋊C4—44no—
68Dic43⋊C4—42no—
69C4×Dic43—22no—
70C4×Dic43—22no—
71C4×Dic43—22no—
72C4×Dic43—42no—
73C4×Dic43—42no—
74C4×Dic43—42no—
75C4×Dic43C2×C812yes—
76C4×Dic43M1612yes—
77C2×C43⋊C8—42no—
78C2×C43⋊C8—42no—
79C2×C43⋊C8—42no—
80C23×C43C2×C22⋊C411yescharacteristic
81Q8×C43—42no—
82Q8×C43—42no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—41no—
89C2×C4×C43—41no—
90C2×C4×C43—41no—
91C2×C4×C43—42no—
92C2×C4×C43C22×C811yescharacteristic
93C2×C4×C43C2×M1611yescharacteristic
94C2×C4×C43#13712yes—
95C2×C4×C43#13712yes—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—22no—
99C2×Dic43—22no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—41no—
103C2×Dic43—41no—
104C2×Dic43—41no—
105C2×Dic43—42no—
106C2×Dic43C22⋊C814yes—
107C2×Dic43#10012yes—
108Dic86—42no—
109Dic86—42no—
110C8×C43—82no—
111C43⋊C8—82no—
112#7605—431nomaximal, Sylow
113C22×C43C2×C22⋊C811yescharacteristic
114C22×C43#41011yescharacteristic
115C22×C43C2×#10011yescharacteristic
116C22×C43#41912yes—
117C22×C43#42112yes—
118C4×C43—21no—
119C4×C43—21no—
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—42no—
123C4×C43—81no—
124Dic43—22no—
125Dic43—24no—
126Dic43—41no—
127Dic43—42no—
128Dic43—81no—
129C4×C4⋊Q8—431no—
130#1839—432no—
131#1272—431no—
132#1272—432no—
133#1272D4311yescharacteristic
134C2×C43#146011yescharacteristic
135C2×C43#147912yes—
136C2×C43#151512yes—
137C2×C43#153611yescharacteristic
138C2×C43#155811yescharacteristic
139C2×C4⋊Q8—431no—
140C2×C4×Q8—431no—
141C2×C4×Q8—431no—
142#391—431no—
143#391C2×D4311yescharacteristic
144#389—862no—
145#384—431no—
146C4×C4⋊C4—862no—
147C43—431no—
148#336—432no—
149#336—862no—
150#336—862no—
151#336C2×D4312yes—
152C43#760511yescharacteristic, complemented, Sylow
153C22×Q8—431no—
154C22×Q8C4×D4311yescharacteristic
155C22×C8—22no—
156C22×C8—862no—
157C4⋊Q8—434no—
158C4⋊Q8—862no—
159C4×Q8—1722no—
160C4×Q8—1722no—
161C2×C4⋊C4—431no—
162C2×C4⋊C4—862no—
163C2×C4⋊C4—861no—
164C2×C4⋊C4—861no—
165C2×C4⋊C4—862no—
166C2×C4⋊C4C4×D4311yescharacteristic
167C2×C42—431no—
168C2×C42—431no—
169C2×C42—432no—
170C2×C42—432no—
171C2×C42—861no—
172C2×C42—861no—
173C2×C42C22×D4311yescharacteristic
174#95—22no—
175#95—862no—
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—432no—
180C2×Q8—861no—
181C2×Q8—1721no—
182C2×Q8—1721no—
183C2×Q8C8×D4312yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—431no—
187C22×C4—432no—
188C22×C4—431no—
189C22×C4—861no—
190C22×C4—861no—
191C22×C4C2×C4×D4311yescharacteristic
192C22×C4D4×D4312yes—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—1722no—
197C2×C8—1722no—
198C2×C8—1722no—
199C4⋊C4—41no—
200C4⋊C4—868no—
201C4⋊C4—1721no—
202C4⋊C4—1722no—
203C4⋊C4—1722no—
204C4⋊C4—1724no—
205C42—41no—
206C42—432no—
207C42—432no—
208C42—862no—
209C42—862no—
210C42—862no—
211C42—1722no—
212C42—1722no—
213C42—1722no—
214C23C22⋊C4×D4311yescharacteristic
215Q8—42no—
216Q8—42no—
217Q8—1722no—
218Q8—1722no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—434no—
229C2×C4—432no—
230C2×C4—862no—
231C2×C4—862no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—861no—
235C2×C4—862no—
236C2×C4—1721no—
237C2×C4—1722no—
238C2×C4—1721no—
239C2×C4—1721no—
240C2×C4C2×C8×D4311yescharacteristic
241C2×C4M16×D4311yescharacteristic
242C2×C4#1306335412yes—
243C2×C4#1306335712yes—
244C8—82no—
245C8—3442no—
246C22C22⋊C8×D4311yescharacteristic
247C22#1458287111yescharacteristic
248C22#100×D4311yescharacteristic
249C22#1458290612yes—
250C22#1458291412yes—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—42no—
256C4—81no—
257C4—864no—
258C4—862no—
259C4—3441no—
260C4—1721no—
261C4—1722no—
262C2#1913291411yescharacteristic
263C2#1913298812yes—
264C2#1913314412yes—
265C2#1913322811yescharacteristic
266C2#1913331911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7605
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
22. #13063323C8semidirect
152. C43#7605semidirect

Maximal subgroups

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

subgroupindex
#191371642
#191347372
#191324212
#191324202
C43×#12722
#760543