Finite Group Databasebeta

← #25006099

Subgroups — #25006099

Order 11008.

334 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 79 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#19143300C211yesmaximal, characteristic
2#19136411C211yesmaximal, characteristic, complemented
3#19132532C212yesmaximal, complemented
4#19132530C212yesmaximal, complemented
5C43×#2166C211yesmaximal, characteristic, complemented
6C2×#13063331C411yescharacteristic
7C22×#10621872C411yescharacteristic
8#14583411C411yescharacteristic
9#14582978—21no—
10#14582978—21no—
11#14582972—21no—
12#14582972—21no—
13#14582926C411yescharacteristic
14#14582867C2211yescharacteristic
15#14582862C2211yescharacteristic
16#14582720—21no—
17#14582681C2212yes—
18#14582677—21no—
19C43×#405C2211yescharacteristic
20C43×#364—21no—
21C43×#349C2212yes—
22C43×#347—21no—
23C2×#10621898C2×C411yescharacteristic
24C22×C4×D43C2×C411yescharacteristic
25#13063331—42no—
26C2×#10621877C2×C411yescharacteristic
27C2×#10621872—21no—
28C2×#10621872—21no—
29C2×#10621872—21no—
30C2×#10621872—42no—
31C22×C43⋊C8C2×C411yescharacteristic
32C2×C8×D43—21no—
33#13063309—21no—
34#13063305—21no—
35#13063300—21no—
36#13063295—21no—
37C4×D172—21no—
38C4×D172—21no—
39#13063265—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42(C2×D43)⋊C8—21no—
43(C2×D43)⋊C8—21no—
44(C2×D43)⋊C8—21no—
45(C2×D43)⋊C8—21no—
46C2×M16×C43C2311yescharacteristic
47C22×C8×C43C2×C411yescharacteristic
48#117×C43C2×C411yescharacteristic
49M32×C43—22no—
50#97×C43D411yescharacteristic
51#97×C43D411yescharacteristic
52C4×C8×C43D411yescharacteristic
53C4×C8×C43D411yescharacteristic
54C23×D43M1611yescharacteristic
55C22×C4×C43C22×C411yescharacteristic
56C2×C22⋊D43—21no—
57C22×Dic43M1611yescharacteristic
58#10621898—41no—
59#10621898—41no—
60C2×D172—21no—
61C2×D172—21no—
62C2×D172M1611yescharacteristic
63C2×C4×D43—21no—
64C2×C4×D43—21no—
65C2×C4×D43—21no—
66C2×C4×D43—41no—
67C2×C4×D43—41no—
68C2×Dic86M1611yescharacteristic
69M16×C43—41no—
70C2×C8×C43—22no—
71C2×C8×C43C22⋊C411yescharacteristic
72C2×C8×C43C22⋊C411yescharacteristic
73C2×C8×C43C2×D411yescharacteristic
74C2×C8×C43C2×D411yescharacteristic
75C4⋊C4×C43—21no—
76C22⋊C4×C43—21no—
77C42×C43C22⋊C411yescharacteristic
78C42×C43C22⋊C411yescharacteristic
79(C2×D43)⋊C4—21no—
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—21no—
82(C2×D43)⋊C4—21no—
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85#10621877—41no—
86C2×C43⋊C8—21no—
87C2×C43⋊C8—21no—
88C2×C43⋊C8—41no—
89#10621872—42no—
90#10621872—42no—
91#10621872—42no—
92C8×D43—42no—
93C16×C43—42no—
94C43⋊C16—42no—
95C23×C43C2×M1611yescharacteristic
96C22×D43—21no—
97C22×D43—21no—
98C22×D43—41no—
99C22×D43—81no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43C2×C22⋊C411yescharacteristic
105C2×C4×C43C2×M1611yescharacteristic
106C22⋊D43—42no—
107C2×Dic43—21no—
108C2×Dic43—21no—
109C2×Dic43—41no—
110D172—41no—
111D172—81no—
112D172—81no—
113C4×D43—42no—
114C4×D43—41no—
115C4×D43—41no—
116C4×D43—41no—
117C4×D43—41no—
118Dic86—41no—
119C8×C43—21no—
120C8×C43—21no—
121C8×C43—21no—
122C8×C43#10012yes—
123C43⋊C8—41no—
124C43⋊C8—41no—
125#11538—431nomaximal, Sylow
126C22×C43—21no—
127C22×C43—41no—
128C22×C43#40711yescharacteristic
129C2×D43—41no—
130C2×D43—41no—
131C2×D43—41no—
132C2×D43—41no—
133C2×D43—41no—
134C2×D43—41no—
135C2×D43—82no—
136C4×C43—21no—
137C4×C43—41no—
138C4×C43—41no—
139C4×C43#41011yescharacteristic
140C4×C43C2×#10011yescharacteristic
141Dic43—41no—
142Dic43—41no—
143#2930—431no—
144#2166—431no—
145#2166D4311yescharacteristic, complemented
146#1321—432no—
147#1320—432no—
148C2×C43—21no—
149C2×C43—41no—
150C2×C43#146611yescharacteristic
151D43—81no—
152D43—81no—
153C2×#131—431no—
154C22×M16—431no—
155#525—431no—
156#436—861no—
157#436—861no—
158#435—861no—
159#435—861no—
160#424—431no—
161#408—431no—
162#407—431no—
163#405C2×D4311yescharacteristic
164#364—21no—
165#364—861no—
166#349—432no—
167#349C2×D4312yes—
168#347—21no—
169#347—861no—
170C43#1153811yescharacteristic, complemented, Sylow
171C2×#41—431no—
172C23×C4—431no—
173#131—1722no—
174C2×M16—431no—
175C2×M16—861no—
176C2×M16—861no—
177C2×M16—861no—
178C2×M16—1722no—
179C2×M16C22×D4311yescharacteristic
180C22×C8—431no—
181C22×C8—861no—
182C22×C8C4×D4311yescharacteristic
183#123—861no—
184C22⋊Q8—861no—
185#121—861no—
186#120—861no—
187C4×D4—861no—
188C4×D4—861no—
189#117C4×D4311yescharacteristic
190M32—22no—
191M32—862no—
192C4⋊C8—861no—
193C4⋊C8—861no—
194C22⋊C8—861no—
195C22⋊C8—861no—
196C22⋊C8—861no—
197C22⋊C8—861no—
198#97D17211yescharacteristic
199#97C22⋊D4311yescharacteristic
200C4×C8D17211yescharacteristic
201C4×C8C22⋊D4311yescharacteristic
202C24—431no—
203#41—1721no—
204#41—1721no—
205C2×Q8—431no—
206C2×D4—431no—
207C2×D4—861no—
208C2×D4—861no—
209C2×D4—861no—
210C22×C4—431no—
211C22×C4—861no—
212C22×C4—861no—
213C22×C4—861no—
214C22×C4—1721no—
215C22×C4—1721no—
216C22×C4C2×C4×D4311yescharacteristic
217M16—41no—
218M16—1722no—
219M16—1722no—
220M16—1722no—
221M16—1721no—
222C2×C8—22no—
223C2×C8—861no—
224C2×C8—861no—
225C2×C8—1722no—
226C2×C8—1721no—
227C2×C8(C2×D43)⋊C411yescharacteristic
228C2×C8(C2×D43)⋊C411yescharacteristic
229C2×C8C2×D17211yescharacteristic
230C2×C8C2×C22⋊D4311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—861no—
233C4⋊C4—861no—
234C22⋊C4—21no—
235C22⋊C4—861no—
236C22⋊C4—861no—
237C22⋊C4—861no—
238C22⋊C4—861no—
239C42(C2×D43)⋊C411yescharacteristic
240C42(C2×D43)⋊C411yescharacteristic
241C16—42no—
242C16—1722no—
243C23—861no—
244C23—861no—
245C23—3441no—
246C23—1721no—
247C23M16×D4311yescharacteristic
248Q8—1721no—
249D4—3441no—
250D4—3441no—
251D4—1721no—
252D4—1722no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—861no—
258C2×C4—861no—
259C2×C4—1722no—
260C2×C4—1721no—
261C2×C4—1721no—
262C2×C4—1721no—
263C2×C4—1721no—
264C2×C4—1721no—
265C2×C4C2×(C2×D43)⋊C411yescharacteristic
266C2×C4M16×D4311yescharacteristic
267C8—21no—
268C8—21no—
269C8—21no—
270C8—1721no—
271C8—1721no—
272C8#1306324112yes—
273C22—21no—
274C22—41no—
275C22—3442no—
276C22—1721no—
277C22—1721no—
278C22—1721no—
279C22—1721no—
280C22—1721no—
281C22—1721no—
282C22#1458286211yescharacteristic
283C4—21no—
284C4—41no—
285C4—41no—
286C4—1721no—
287C4—1721no—
288C4#1458287211yescharacteristic
289C4C2×#1306324111yescharacteristic
290C2—21no—
291C2—41no—
292C2—3441no—
293C2—3441no—
294C2#1913293511yescharacteristic
subgroupG/H
centerC4#14582872
commutatorC22×C4×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#2166C2
socleC2×C43#1466
prime radical#14583411C4
cosocleC2×M16×C43C23
hypercenter#2166D43
hypocenterC43#11538
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C8 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #19136411C2semidirect
3. #19132532C2semidirect
4. #19132530C2semidirect
5. C43×#2166C2semidirect
145. #2166D43semidirect
170. C43#11538semidirect

Maximal subgroups

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

subgroupindex
#191433002
#191364112
#191325322
#191325302
C43×#21662
#1153843