Finite Group Databasebeta

← #25005910

Subgroups — #25005910

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#19143312C211yesmaximal, characteristic
2#19136214C212yesmaximal, complemented
3#19132546C211yesmaximal, characteristic, complemented
4#19132532C212yesmaximal, complemented
5C43×#1327C211yesmaximal, characteristic, complemented
6C2×#13063333C411yescharacteristic
7C2×#13063333C2211yescharacteristic
8#14583449C411yescharacteristic
9M32×D43—22no—
10#14582969—22no—
11#14582969—22no—
12#14582867C411yescharacteristic
13#14582867C2211yescharacteristic
14C2×#13063236C411yescharacteristic
15#14582681C2212yes—
16#14582680—22no—
17C43×#423C2211yescharacteristic
18C43×#349C2212yes—
19C2×#10621898C2×C411yescharacteristic
20C2×#10621898C2×C411yescharacteristic
21#13063333—42no—
22#13063333—42no—
23C2×#10621872—21no—
24C2×#10621872D412yes—
25C22×C43⋊C8C2×C411yescharacteristic
26C22×C43⋊C8C2×C411yescharacteristic
27C2×C8×D43—21no—
28C2×C8×D43D412yes—
29#13063325C811yescharacteristic
30#13063322C811yescharacteristic
31#13063313C811yescharacteristic
32#13063313C811yescharacteristic
33#13063299—22no—
34C4×D172—22no—
35#13063265—22no—
36#13063264—42no—
37C16×D43—42no—
38(C2×D43)⋊C8—22no—
39(C2×D43)⋊C8—22no—
40#13063236—21no—
41#13063236—21no—
42C2×M16×C43C2×C411yescharacteristic
43C2×M16×C43C2311yescharacteristic
44C2×C42×C43C2×C411yescharacteristic
45M32×C43—22no—
46C4⋊C8×C43—22no—
47C22×C4×C43—21no—
48C22×C4×C43C22×C411yescharacteristic
49C2×C22⋊D43—21no—
50C2×C22⋊D43M1612yes—
51#10621898—41no—
52#10621898—41no—
53#10621898—41no—
54#10621898—41no—
55C2×D172—22no—
56C2×D172C2×C811yescharacteristic
57C2×D172C2×C811yescharacteristic
58C2×C4×D43—21no—
59C2×C4×D43C22⋊C412yes—
60C2×Dic86C2×C811yescharacteristic
61C2×Dic86C2×C811yescharacteristic
62M16×C43—41no—
63M16×C43—41no—
64C2×C8×C43—21no—
65C2×C8×C43C2×D412yes—
66C42×C43—21no—
67C42×C43C2×C811yescharacteristic
68C42×C43C2×C811yescharacteristic
69(C2×D43)⋊C4—22no—
70(C2×D43)⋊C4—22no—
71C4⋊Dic43—22no—
72C2×C43⋊C8—22no—
73C2×C43⋊C8—21no—
74C2×C43⋊C8—41no—
75C2×C43⋊C8C22⋊C411yescharacteristic
76C2×C43⋊C8C22⋊C411yescharacteristic
77#10621872—42no—
78#10621872—42no—
79C8×D43—22no—
80C8×D43—22no—
81C8×D43—42no—
82C16×C43—42no—
83C43⋊C16—42no—
84C23×C43C2×M1611yescharacteristic
85C22×D43—21no—
86C22×D43C22⋊C812yes—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—81no—
92C2×C4×C43C2×C22⋊C411yescharacteristic
93C2×C4×C43C22×C811yescharacteristic
94C22⋊D43—42no—
95C22⋊D43—42no—
96C2×Dic43—21no—
97C2×Dic43C22⋊C812yes—
98D172—41no—
99D172—41no—
100D172—82no—
101C4×D43—22no—
102C4×D43—22no—
103C4×D43—41no—
104C4×D43—41no—
105Dic86—41no—
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×C43C2×C22⋊C811yescharacteristic
116C2×D43—22no—
117C2×D43—42no—
118C2×D43—42no—
119C2×D43—41no—
120C4×C43—21no—
121C4×C43—41no—
122C4×C43—41no—
123C4×C43C2×#9911yescharacteristic
124C4×C43#41311yescharacteristic
125Dic43—22no—
126Dic43—41no—
127#2932—431no—
128#2115—432no—
129#1327—431no—
130#1327D4311yescharacteristic, complemented
131#1321—432no—
132C2×C43—21no—
133C2×C43—41no—
134C2×C43#145911yescharacteristic
135D43—42no—
136D43—81no—
137C2×#131—431no—
138C2×#131—431no—
139#532—431no—
140C2×M32—862no—
141#435—862no—
142#435—862no—
143#423C2×D4311yescharacteristic
144#408—431no—
145#408—431no—
146C2×#97—431no—
147#349—432no—
148#349—862no—
149#349C2×D4312yes—
150C43#1148611yescharacteristic, complemented, Sylow
151C2×#41—431no—
152C2×#41—431no—
153#131—1722no—
154#131—1722no—
155C2×M16—432no—
156C2×M16—861no—
157C2×M16C4×D4311yescharacteristic
158C2×M16C22×D4311yescharacteristic
159C22×C8—431no—
160C22×C8—432no—
161C22×C8—431no—
162C22×C8—861no—
163C4⋊Q8—431no—
164#127—431no—
165#124—431no—
166#124—431no—
167#121—862no—
168C4×D4—862no—
169C2×C42C4×D4311yescharacteristic
170M32—22no—
171M32—862no—
172M32—1722no—
173C2×C16—1722no—
174C4⋊C8—22no—
175C22⋊C8—862no—
176C22⋊C8—862no—
177#97—861no—
178#97—861no—
179#41—1721no—
180#41—1721no—
181#41—1721no—
182#41—1721no—
183C2×Q8—431no—
184C2×Q8—431no—
185C2×D4—432no—
186C2×D4—431no—
187C2×D4—431no—
188C2×D4—862no—
189C2×D4—861no—
190C22×C4—21no—
191C22×C4—432no—
192C22×C4—861no—
193C22×C4C2×C4×D4311yescharacteristic
194M16—41no—
195M16—41no—
196M16—1722no—
197M16—1722no—
198C2×C8—21no—
199C2×C8—431no—
200C2×C8—431no—
201C2×C8—862no—
202C2×C8—862no—
203C2×C8—862no—
204C2×C8—861no—
205C2×C8—1722no—
206C2×C8—1721no—
207C2×C8D4×D4312yes—
208C4⋊C4—862no—
209C22⋊C4—862no—
210C22⋊C4—862no—
211C42—21no—
212C42C8×D4311yescharacteristic
213C42C8×D4311yescharacteristic
214C16—42no—
215C16—1722no—
216C23—432no—
217C23—861no—
218C23M16×D4311yescharacteristic
219Q8—1721no—
220Q8—1721no—
221D4—3442no—
222D4—1721no—
223D4—1721no—
224D4—1722no—
225D4—1722no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—81no—
231C2×C4—432no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—861no—
235C2×C4—1721no—
236C2×C4—1721no—
237C2×C4C22⋊C4×D4311yescharacteristic
238C2×C4C2×C8×D4311yescharacteristic
239C8—22no—
240C8—41no—
241C8—432no—
242C8—861no—
243C8—1721no—
244C22—21no—
245C22—41no—
246C22—862no—
247C22—1722no—
248C22—1722no—
249C22—1721no—
250C22C22⋊C8×D4311yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—862no—
255C4—1721no—
256C4#99×D4311yescharacteristic
257C4#1458288211yescharacteristic
258C2—21no—
259C2—41no—
260C2—3441no—
261C2—1722no—
262C2#1913291211yescharacteristic
subgroupG/H
centerC4#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×M16C22×D43
FittingC43×#1327C2
socleC2×C43#1459
prime radical#14583449C4
cosocleC2×M16×C43C23
hypercenter#1327D43
hypocenterC43#11486
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #19136214C2semidirect
3. #19132546C2semidirect
4. #19132532C2semidirect
5. C43×#1327C2semidirect
130. #1327D43semidirect
150. C43#11486semidirect

Maximal subgroups

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

subgroupindex
#191433122
#191362142
#191325462
#191325322
C43×#13272
#1148643