Finite Group Databasebeta

← #25013416

Subgroups — #25013416

Order 11008.

416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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#19136260C211yesmaximal, characteristic
2#19134979C211yesmaximal, characteristic
3#19134880C212yesmaximal, complemented
4#19132716C212yesmaximal, complemented
5C43×#2980C211yesmaximal, characteristic
6#14583666C2211yescharacteristic
7#14582925—22no—
8#14582916—21no—
9#14582873C2211yescharacteristic
10#14582873C2212yes—
11#14582694C412yescomplemented
12#14582692C412yescomplemented
13#14582671—22no—
14#14582659—21no—
15C43×#532C2211yescharacteristic
16C43×#435—22no—
17C43×#435—22no—
18C43×#432—21no—
19C43×#408—21no—
20C43×#408C2212yes—
21#13063332—42no—
22C2×#10621877—22no—
23C2×#10621877—21no—
24#13063284—22no—
25#13063284—21no—
26Dic43⋊C8—44no—
27#13063252—42no—
28#13063240—22no—
29#13063240—22no—
30#13063240C2×C414yes—
31C2×#41×C43D411yescharacteristic
32C2×#41×C43C2311yescharacteristic
33C2×M16×C43—21no—
34C2×M16×C43D412yes—
35C22×C8×C43—21no—
36C22×C8×C43D412yes—
37C4⋊Q8×C43Q811yescharacteristic
38#127×C43C2×C411yescharacteristic
39#124×C43C2×C411yescharacteristic
40#124×C43Q811yescharacteristic
41#121×C43—22no—
42C4×D4×C43—22no—
43C2×C42×C43D411yescharacteristic
44C4⋊C8×C43—21no—
45C4⋊C8×C43—21no—
46C22⋊C8×C43—22no—
47C22⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49#97×C43—22no—
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
65M16×C43—42no—
66M16×C43—81no—
67C2×C8×C43—22no—
68C2×C8×C43—22no—
69C2×C8×C43—42no—
70C2×C8×C43—81no—
71C4⋊C4×C43—22no—
72C22⋊C4×C43—22no—
73C22⋊C4×C43—22no—
74C42×C43—21no—
75C42×C43C4⋊C411yescharacteristic
76C42×C43C4⋊C411yescharacteristic
77C22⋊Dic43—24no—
78C22⋊Dic43—41no—
79C4⋊Dic43—42no—
80C4⋊Dic43—41no—
81C4×Dic43—42no—
82C4×Dic43—41no—
83#10621877—22no—
84#10621877—42no—
85#10621877—41no—
86C2×C43⋊C8—24no—
87C2×C43⋊C8—41no—
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—81no—
108C2×C4×C43C2×C4⋊C411yescharacteristic
109C2×C4×C43#12011yescharacteristic
110C2×C4×C43C22⋊Q812yes—
111C2×Dic43—44no—
112C2×Dic43—81no—
113C8×C43—42no—
114C8×C43—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×C43B(4,𝔽2)11yescharacteristic
130C4×C43#45811yescharacteristic
131Dic43—84no—
132Dic43—161no—
133#2980D4311yescharacteristic
134#2126—431no—
135#1884—431no—
136#1868—432no—
137#1391—432no—
138C2×C43—21no—
139C2×C43—42no—
140C2×C43—41no—
141C2×C43—81no—
142C2×C43#186711yescharacteristic
143#568—431no—
144#532C2×D4311yescharacteristic
145#435—22no—
146#435—22no—
147#432—21no—
148#424—862no—
149#421—861no—
150#410—432no—
151#410—431no—
152#408—21no—
153#408C2×D4312yes—
154#354—432no—
155#353—432no—
156#344—862no—
157#339—861no—
158C43#1296911yescharacteristic, complemented, Sylow
159C2×#41C22⋊D4311yescharacteristic
160C2×#41C22×D4311yescharacteristic
161#131—1722no—
162C2×M16—21no—
163C2×M16—862no—
164C2×M16—861no—
165C2×M16C22⋊D4312yes—
166C22×C8—21no—
167C22×C8C22⋊D4312yes—
168C4⋊Q8Dic8611yescharacteristic
169#127C4×D4311yescharacteristic
170#124Dic8611yescharacteristic
171#124C4×D4311yescharacteristic
172#121—22no—
173C4×D4—22no—
174#117—862no—
175#117—861no—
176C2×C42C22⋊D4311yescharacteristic
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—1724no—
180#104—1722no—
181#99—434no—
182#99—862no—
183#99—862no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187#97—22no—
188#41—41no—
189#41—41no—
190#41—41no—
191#41—41no—
192C2×Q8Dic43⋊C411yescharacteristic
193C2×Q8C2×Dic8611yescharacteristic
194C2×D4—22no—
195C2×D4—21no—
196C2×D4Dic43⋊C411yescharacteristic
197C2×D4C2×C4×D4311yescharacteristic
198C2×D4#1062189812yes—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4C2×C22⋊D4311yescharacteristic
202C22×C4C2×C22⋊D4312yes—
203M16—42no—
204M16—81no—
205M16—862no—
206M16—1722no—
207M16—1721no—
208C2×C8—22no—
209C2×C8—22no—
210C2×C8—42no—
211C2×C8—81no—
212C2×C8—864no—
213C2×C8—1721no—
214C4⋊C4—22no—
215C4⋊C4—1721no—
216C4⋊C4—1722no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—864no—
220C22⋊C4—1721no—
221C42—21no—
222C42—1721no—
223C42—1722no—
224C42Dic43⋊C411yescharacteristic
225C42Dic43⋊C411yescharacteristic
226C23—21no—
227C23C4×C22⋊D4312yes—
228C23#1306330811yescharacteristic
229Q8—41no—
230Q8—41no—
231D4—41no—
232D4—42no—
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—81no—
246C2×C4—3441no—
247C2×C4—1724no—
248C2×C4C2×Dic43⋊C411yescharacteristic
249C2×C4#1306329411yescharacteristic
250C2×C4#1306330412yes—
251C8—42no—
252C8—42no—
253C8—1722no—
254C22—21no—
255C22—22no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22#1458277211yescharacteristic
261C4—21no—
262C4—22no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—3444no—
267C4—6881no—
268C4#1458308611yescharacteristic
269C4#1458308911yescharacteristic
270C2—21no—
271C2—42no—
272C2—41no—
273C2—81no—
274C2#1913487611yescharacteristic
subgroupG/H
centerC4#14583086
commutatorC2×D4×C43C22×C4
FrattiniC2×#41C22×D43
FittingC43×#2980C2
socleC2×C43#1867
prime radicalC43×#532C22
cosocleC2×#41×C43C23
hypercenter#2980D43
hypocenterC43#12969
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2980

Complements

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

NH ≅ G/Ntype
3. #19134880C2semidirect
4. #19132716C2semidirect
11. #14582694C4semidirect
12. #14582692C4semidirect
158. C43#12969semidirect

Maximal subgroups

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

subgroupindex
#191362602
#191349792
#191348802
#191327162
C43×#29802
#1296943