Finite Group Databasebeta

← #25013418

Subgroups — #25013418

Order 11008.

416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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#19143666C211yesmaximal, characteristic
2#19134979C211yesmaximal, characteristic
3#19134883C212yesmaximal, complemented
4#19132715C212yesmaximal, complemented
5C43×#2126C211yesmaximal, characteristic
6#14583666C2211yescharacteristic
7#14582971—22no—
8#14582971—22no—
9#14582956—21no—
10#14582926—22no—
11#14582916—21no—
12#14582873C2211yescharacteristic
13#14582866—21no—
14#14582866C2212yes—
15#14582669—22no—
16#14582659—21no—
17C43×#532C2211yescharacteristic
18C43×#410C2212yes—
19C43×#354C412yescomplemented
20C43×#353C412yescomplemented
21#13063332—42no—
22C2×#10621877—22no—
23C2×#10621877—21no—
24C2×#10621877—21no—
25C2×#10621877D412yes—
26C22×C43⋊C8—21no—
27C22×C43⋊C8D412yes—
28#13063284—21no—
29C4⋊(C43⋊C8)—21no—
30C4⋊(C43⋊C8)—21no—
31C4⋊(C43⋊C8)—44no—
32#13063252—42no—
33#13063240—22no—
34C22⋊(C43⋊C8)—22no—
35C22⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)—22no—
37#13063236—22no—
38C2×#41×C43D411yescharacteristic
39C2×#41×C43C2311yescharacteristic
40C4⋊Q8×C43Q811yescharacteristic
41#127×C43C2×C411yescharacteristic
42#124×C43C2×C411yescharacteristic
43#124×C43Q811yescharacteristic
44#121×C43—22no—
45C4×D4×C43—22no—
46#117×C43—22no—
47C2×C42×C43D411yescharacteristic
48#99×C43—22no—
49#99×C43C2×C414yes—
50#41×C43—41no—
51#41×C43—41no—
52#41×C43—41no—
53#41×C43—41no—
54C2×Q8×C43C4⋊C411yescharacteristic
55C2×Q8×C43C2×Q811yescharacteristic
56C2×D4×C43—22no—
57C2×D4×C43—21no—
58C2×D4×C43C4⋊C411yescharacteristic
59C2×D4×C43C22×C411yescharacteristic
60C2×D4×C43#4112yes—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43C2×D412yes—
64C22×C4×C43C2×D411yescharacteristic
65C4⋊C4×C43—22no—
66C4⋊C4×C43—42no—
67C22⋊C4×C43—22no—
68C22⋊C4×C43—22no—
69C22⋊C4×C43—24no—
70C42×C43—21no—
71C42×C43—42no—
72C42×C43C4⋊C411yescharacteristic
73C42×C43C4⋊C411yescharacteristic
74C22⋊Dic43—41no—
75C4⋊Dic43—41no—
76C4×Dic43—41no—
77#10621877—22no—
78#10621877—42no—
79#10621877—41no—
80#10621877—42no—
81#10621877—81no—
82C2×C43⋊C8—24no—
83C2×C43⋊C8—22no—
84C2×C43⋊C8—22no—
85C2×C43⋊C8—41no—
86C2×C43⋊C8—42no—
87C2×C43⋊C8—81no—
88C23×C43—21no—
89C23×C43C4×D412yes—
90C23×C43#12311yescharacteristic
91Q8×C43—41no—
92Q8×C43—41no—
93D4×C43—41no—
94D4×C43—42no—
95D4×C43—41no—
96D4×C43—81no—
97D4×C43—82no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—44no—
108C2×C4×C43—81no—
109C2×C4×C43C2×C4⋊C411yescharacteristic
110C2×C4×C43#12011yescharacteristic
111C2×C4×C43C22⋊Q812yes—
112C2×Dic43—81no—
113C43⋊C8—42no—
114C43⋊C8—42no—
115C43⋊C8—42no—
116#12969—431nomaximal, Sylow
117C22×C43—22no—
118C22×C43—21no—
119C22×C43—42no—
120C22×C43—41no—
121C22×C43—42no—
122C22×C43—41no—
123C22×C43#38511yescharacteristic
124C4×C43—21no—
125C4×C43—22no—
126C4×C43—41no—
127C4×C43—41no—
128C4×C43—41no—
129C4×C43—84no—
130C4×C43B(4,𝔽2)11yescharacteristic
131C4×C43#45811yescharacteristic
132Dic43—161no—
133#2980—431no—
134#2126D4311yescharacteristic
135#1884—431no—
136#1868—432no—
137#1391—432no—
138C2×C43—21no—
139C2×C43—41no—
140C2×C43—42no—
141C2×C43—81no—
142C2×C43#186711yescharacteristic
143#568—431no—
144#532C2×D4311yescharacteristic
145#435—862no—
146#435—862no—
147#432—861no—
148#424—862no—
149#421—861no—
150#410—431no—
151#410C2×D4312yes—
152#408—432no—
153#408—861no—
154#354Dic4312yescomplemented
155#353Dic4312yescomplemented
156#344—862no—
157#339—861no—
158C43#1296911yescharacteristic, complemented, Sylow
159C2×#41D17211yescharacteristic
160C2×#41C22×D4311yescharacteristic
161#131—1722no—
162C2×M16—432no—
163C2×M16—861no—
164C2×M16—862no—
165C2×M16—861no—
166C22×C8—432no—
167C22×C8—861no—
168C4⋊Q8Dic8611yescharacteristic
169#127C2×Dic4311yescharacteristic
170#124Dic8611yescharacteristic
171#124C2×Dic4311yescharacteristic
172#121—22no—
173C4×D4—22no—
174#117—22no—
175#117—861no—
176C2×C42D17211yescharacteristic
177C4⋊C8—861no—
178C4⋊C8—861no—
179C4⋊C8—1724no—
180#104—1722no—
181#99—22no—
182#99—862no—
183#99C2×Dic4314yes—
184C22⋊C8—862no—
185C22⋊C8—862no—
186C22⋊C8—862no—
187#97—862no—
188#41—41no—
189#41—41no—
190#41—41no—
191#41—41no—
192C2×Q8C4⋊Dic4311yescharacteristic
193C2×Q8C2×Dic8611yescharacteristic
194C2×D4—22no—
195C2×D4—21no—
196C2×D4C4⋊Dic4311yescharacteristic
197C2×D4#1062190012yes—
198C2×D4C22×Dic4311yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4C2×D17211yescharacteristic
202C22×C4D4×D4312yes—
203M16—862no—
204M16—3441no—
205M16—1722no—
206M16—1721no—
207M16—1722no—
208C2×C8—864no—
209C2×C8—862no—
210C2×C8—862no—
211C2×C8—3441no—
212C2×C8—1721no—
213C2×C8—1722no—
214C4⋊C4—22no—
215C4⋊C4—42no—
216C4⋊C4—1721no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—24no—
220C22⋊C4—1721no—
221C42—21no—
222C42—42no—
223C42—1721no—
224C42C4⋊Dic4311yescharacteristic
225C42C4⋊Dic4311yescharacteristic
226C23—21no—
227C23D4×Dic4312yes—
228C23#1306330911yescharacteristic
229Q8—41no—
230Q8—41no—
231D4—42no—
232D4—41no—
233D4—41no—
234D4—81no—
235D4—82no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—44no—
246C2×C4—81no—
247C2×C4—3441no—
248C2×C4C2×C4⋊Dic4311yescharacteristic
249C2×C4#1306329511yescharacteristic
250C2×C4#1306330212yes—
251C8—1722no—
252C8—1722no—
253C8—1722no—
254C22—22no—
255C22—21no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22#1458277411yescharacteristic
261C4—21no—
262C4—22no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—84no—
267C4—6881no—
268C4#1458308711yescharacteristic
269C4#1458309011yescharacteristic
270C2—21no—
271C2—42no—
272C2—41no—
273C2—81no—
274C2#1913487811yescharacteristic
subgroupG/H
centerC4#14583087
commutatorC2×D4×C43C22×C4
FrattiniC2×#41C22×D43
FittingC43×#2126C2
socleC2×C43#1867
prime radicalC43×#532C22
cosocleC2×#41×C43C23
hypercenter#2126D43
hypocenterC43#12969
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2126

Complements

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

NH ≅ G/Ntype
3. #19134883C2semidirect
4. #19132715C2semidirect
19. C43×#354C4semidirect
20. C43×#353C4semidirect
154. #354Dic43semidirect
155. #353Dic43semidirect
158. C43#12969semidirect

Maximal subgroups

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

subgroupindex
#191436662
#191349792
#191348832
#191327152
C43×#21262
#1296943