Finite Group Databasebeta

← #25005908

Subgroups — #25005908

Order 11008.

364 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 83 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#19143310C211yesmaximal, characteristic
2#19136214C212yesmaximal, complemented
3#19132545C212yesmaximal, complemented
4#19132533C211yesmaximal, characteristic, complemented
5C43×#1321C211yesmaximal, characteristic, complemented
6C2×#13063333C2211yescharacteristic
7C2×#13063332C411yescharacteristic
8#14583445C411yescharacteristic
9M32×D43—22no—
10#14582973—22no—
11#14582967—22no—
12#14582922C2211yescharacteristic
13#14582865C411yescharacteristic
14C2×#13063235C411yescharacteristic
15#14582681C2212yes—
16#14582680—22no—
17C43×#408C2211yescharacteristic
18C43×#349C2212yes—
19C2×#10621898C2×C411yescharacteristic
20#13063333—42no—
21#13063332—42no—
22C2×#10621877—21no—
23C2×#10621877C2×C411yescharacteristic
24C2×#10621872D412yes—
25C22×C43⋊C8—21no—
26C22×C43⋊C8C2×C411yescharacteristic
27C2×C8×D43D412yes—
28#13063323C811yescharacteristic
29#13063321C811yescharacteristic
30#13063314C811yescharacteristic
31#13063312C811yescharacteristic
32#13063297—22no—
33C4×C22⋊D43—22no—
34C2×C4×Dic43C2×C411yescharacteristic
35#13063265—22no—
36#13063264—42no—
37C16×D43—42no—
38Dic43⋊C8—22no—
39(C2×D43)⋊C8—22no—
40#13063235—21no—
41#13063235—21no—
42C2×#41×C43C2×C411yescharacteristic
43C2×M16×C43C2311yescharacteristic
44C22×C8×C43C2×C411yescharacteristic
45M32×C43—22no—
46C22⋊C8×C43—22no—
47#41×C43—41no—
48#41×C43—41no—
49C2×Q8×C43C2×C811yescharacteristic
50C2×D4×C43—21no—
51C2×D4×C43C2×C811yescharacteristic
52C22×C4×C43—21no—
53C22×C4×C43C22×C411yescharacteristic
54C2×C22⋊D43—22no—
55C2×C22⋊D43M1612yes—
56C22×Dic43—21no—
57#10621898—41no—
58#10621898—41no—
59C2×D172C2×C811yescharacteristic
60C2×C4×D43C22⋊C412yes—
61C2×Dic86C2×C811yescharacteristic
62M16×C43—41no—
63C2×C8×C43—21no—
64C2×C8×C43—41no—
65C2×C8×C43C2×D412yes—
66C22⋊Dic43—22no—
67(C2×D43)⋊C4—22no—
68Dic43⋊C4—22no—
69C4×Dic43—21no—
70C4×Dic43C2×C811yescharacteristic
71C4×Dic43C2×C811yescharacteristic
72#10621877—42no—
73#10621877—41no—
74C2×C43⋊C8—22no—
75C2×C43⋊C8—21no—
76C2×C43⋊C8—42no—
77C2×C43⋊C8C22⋊C411yescharacteristic
78C2×C43⋊C8C22⋊C411yescharacteristic
79#10621872—42no—
80C8×D43—22no—
81C8×D43—22no—
82C16×C43—42no—
83C43⋊C16—42no—
84C23×C43—21no—
85C23×C43C2×M1611yescharacteristic
86C22×D43C22⋊C812yes—
87Q8×C43—41no—
88D4×C43—41no—
89D4×C43—42no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43C2×C22⋊C411yescharacteristic
96C2×C4×C43C22×C811yescharacteristic
97C22⋊D43—42no—
98C22⋊D43—82no—
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—81no—
102C2×Dic43C22⋊C812yes—
103D172—41no—
104C4×D43—22no—
105C4×D43—22no—
106Dic86—41no—
107C8×C43—22no—
108C8×C43—41no—
109C43⋊C8—21no—
110C43⋊C8—41no—
111C43⋊C8#9912yes—
112#11486—431nomaximal, Sylow
113C22×C43—21no—
114C22×C43—41no—
115C22×C43—42no—
116C22×C43—41no—
117C22×C43C2×C22⋊C811yescharacteristic
118C2×D43—22no—
119C2×D43—42no—
120C4×C43—21no—
121C4×C43—41no—
122C4×C43C2×#9911yescharacteristic
123C4×C43#41311yescharacteristic
124Dic43—22no—
125Dic43—41no—
126Dic43—41no—
127#2932—431no—
128#2115—432no—
129#1327—432no—
130#1321—431no—
131#1321D4311yescharacteristic, complemented
132C2×C43—21no—
133C2×C43—41no—
134C2×C43—81no—
135C2×C43#145911yescharacteristic
136D43—42no—
137C2×#131—431no—
138C2×#131—431no—
139#532—431no—
140C2×M32—862no—
141#435—862no—
142#435—862no—
143#423—431no—
144#408—431no—
145#408C2×D4311yescharacteristic
146C2×#97—431no—
147#349—432no—
148#349—862no—
149#349C2×D4312yes—
150C43#1148611yescharacteristic, complemented, Sylow
151C2×#41—431no—
152C2×#41C4×D4311yescharacteristic
153#131—1722no—
154#131—1722no—
155C2×M16—432no—
156C2×M16—431no—
157C2×M16—861no—
158C2×M16C22×D4311yescharacteristic
159C22×C8—431no—
160C22×C8—432no—
161C22×C8—861no—
162C22×C8C4×D4311yescharacteristic
163C4⋊Q8—431no—
164#127—431no—
165#124—431no—
166#124—431no—
167#121—862no—
168C4×D4—862no—
169C2×C42—431no—
170M32—22no—
171M32—862no—
172M32—1722no—
173C2×C16—1722no—
174C4⋊C8—862no—
175C22⋊C8—22no—
176C22⋊C8—862no—
177#97—861no—
178#97—861no—
179#41—41no—
180#41—41no—
181#41—1721no—
182#41—1721no—
183C2×Q8—431no—
184C2×Q8C8×D4311yescharacteristic
185C2×D4—21no—
186C2×D4—432no—
187C2×D4—431no—
188C2×D4—862no—
189C2×D4C8×D4311yescharacteristic
190C22×C4—21no—
191C22×C4—432no—
192C22×C4—861no—
193C22×C4C2×C4×D4311yescharacteristic
194M16—41no—
195M16—1722no—
196M16—1722no—
197M16—1721no—
198C2×C8—21no—
199C2×C8—41no—
200C2×C8—431no—
201C2×C8—431no—
202C2×C8—862no—
203C2×C8—862no—
204C2×C8—862no—
205C2×C8—861no—
206C2×C8—1722no—
207C2×C8D4×D4312yes—
208C4⋊C4—862no—
209C22⋊C4—862no—
210C22⋊C4—862no—
211C42—431no—
212C42—431no—
213C42—861no—
214C16—42no—
215C16—1722no—
216C23—21no—
217C23—432no—
218C23M16×D4311yescharacteristic
219Q8—41no—
220Q8—1721no—
221D4—41no—
222D4—42no—
223D4—3442no—
224D4—1721no—
225D4—1722no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—432no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—861no—
235C2×C4—861no—
236C2×C4—3441no—
237C2×C4C22⋊C4×D4311yescharacteristic
238C2×C4C2×C8×D4311yescharacteristic
239C8—22no—
240C8—41no—
241C8—432no—
242C8—861no—
243C8—1721no—
244C22—21no—
245C22—41no—
246C22—42no—
247C22—41no—
248C22—862no—
249C22—1722no—
250C22C22⋊C8×D4311yescharacteristic
251C4—21no—
252C4—41no—
253C4—862no—
254C4—1721no—
255C4—1721no—
256C4#99×D4311yescharacteristic
257C4#1458288011yescharacteristic
258C2—21no—
259C2—41no—
260C2—81no—
261C2—1722no—
262C2#1913291011yescharacteristic
subgroupG/H
centerC4#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×M16C22×D43
FittingC43×#1321C2
socleC2×C43#1459
prime radical#14583445C4
cosocleC2×M16×C43C23
hypercenter#1321D43
hypocenterC43#11486
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #19136214C2semidirect
3. #19132545C2semidirect
4. #19132533C2semidirect
5. C43×#1321C2semidirect
131. #1321D43semidirect
150. C43#11486semidirect

Maximal subgroups

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

subgroupindex
#191433102
#191362142
#191325452
#191325332
C43×#13212
#1148643