Finite Group Databasebeta

← #25008665

Subgroups — #25008665

Order 11008.

466 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135636C211yesmaximal, characteristic
2#19133597C212yesmaximal, complemented
3#19132601C212yesmaximal, complemented
4#19132527C211yesmaximal, characteristic, complemented
5C43×#2724C211yesmaximal, characteristic, complemented
6C2×#13063351—21no—
7#14583480C2211yescharacteristic
8#14583212—22no—
9C2×#13063253—21no—
10#14582668C2211yescharacteristic
11#14582632—22no—
12#14582625C2212yes—
13C2×#123×C43—21no—
14C43×#398C2212yes—
15C43×#397—22no—
16C43×#390C2211yescharacteristic
17C43×#389—21no—
18C43×#385—22no—
19C2×#10621898—21no—
20#13063351—42no—
21#13063351—42no—
22C2×#10621883—41no—
23C2×#10621882—41no—
24C2×#10621877—21no—
25#13063305—41no—
26#13063300—41no—
27#13063299—22no—
28#13063258—42no—
29#13063253—42no—
30#13063245—42no—
31C22⋊(C43⋊C8)—22no—
32C22×D4×C43D411yescharacteristic
33C23×C4×C43—21no—
34#123×C43—42no—
35#123×C43—42no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43D412yes—
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—22no—
44C2×C42×C43D411yescharacteristic
45#95×C43—22no—
46#95×C43—22no—
47#95×C43D412yes—
48C24×C43—21no—
49C2×D4×C43—21no—
50C2×D4×C43—41no—
51C2×D4×C43—41no—
52C2×D4×C43D812yes—
53C22×C4×C43—21no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—42no—
57C22×C4×C43—81no—
58C22×C4×C43—81no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D412yes—
61C2×C22⋊D43—41no—
62#10621898—41no—
63#10621898—41no—
64#10621898—41no—
65#10621898—41no—
66C2×D172—21no—
67C2×D172—22no—
68C2×C4×D43—41no—
69C2×Dic86—21no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—42no—
72C4⋊C4×C43—42no—
73C4⋊C4×C43—42no—
74C4⋊C4×C43—42no—
75C4⋊C4×C43—81no—
76C22⋊C4×C43—42no—
77C22⋊C4×C43—44no—
78C22⋊C4×C43—44no—
79C42×C43—41no—
80#10621883—44no—
81#10621882—44no—
82(C2×D43)⋊C4—42no—
83C4⋊Dic43—22no—
84#10621877—22no—
85#10621877—41no—
86C2×C43⋊C8—41no—
87C2×C43⋊C8—42no—
88C23×C43—22no—
89C23×C43—42no—
90C23×C43—42no—
91C23×C43—41no—
92C23×C43—41no—
93C23×C43#12011yescharacteristic
94C22×D43—41no—
95D4×C43—42no—
96D4×C43—81no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43—84no—
111C2×C4×C43C2×D811yescharacteristic
112C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
113C22⋊D43—81no—
114C22⋊D43—81no—
115C2×Dic43—41no—
116D172—41no—
117D172—41no—
118D172—82no—
119C4×D43—81no—
120C4×D43—81no—
121Dic86—41no—
122Dic86—41no—
123C43⋊C8—42no—
124C43⋊C8—82no—
125#12097—431nomaximal, Sylow
126C22×C43—21no—
127C22×C43—21no—
128C22×C43—44no—
129C22×C43—42no—
130C22×C43—82no—
131C22×C43—81no—
132C22×C43—81no—
133C22×C43#44711yescharacteristic
134C22×C43#45311yescharacteristic
135C22×C43B(4,𝔽2)11yescharacteristic
136C2×D43—81no—
137C2×D43—81no—
138C2×D43—81no—
139C4×C43—21no—
140C4×C43—21no—
141C4×C43—42no—
142C4×C43—42no—
143C4×C43—82no—
144C4×C43—82no—
145Dic43—81no—
146#2724D4311yescharacteristic, complemented
147#2006—431no—
148#1610—432no—
149#1346—432no—
150#1318—431no—
151C2×C43—21no—
152C2×C43—21no—
153C2×C43—82no—
154C2×C43#159511yescharacteristic
155C2×C43#219811yescharacteristic
156C2×C43#220311yescharacteristic
157D43—161no—
158C2×AGL(1,ℤ/8)—861no—
159#537—431no—
160C2×#123—21no—
161#480—862no—
162C2×#104—861no—
163#398C2×D4312yes—
164#397—22no—
165#390C2×D4311yescharacteristic
166#389—21no—
167#385—22no—
168#343—431no—
169#327—862no—
170#324—432no—
171C43#1209711yescharacteristic, complemented, Sylow
172C2×#41—861no—
173C22×D4C22⋊D4311yescharacteristic
174C23×C4—21no—
175AGL(1,ℤ/8)—1722no—
176AGL(1,ℤ/8)—1722no—
177C2×SD16—1721no—
178C2×D8—1721no—
179C2×M16—861no—
180#123—42no—
181#123—42no—
182C22⋊Q8—1721no—
183#121—862no—
184#121—1721no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C22⋊D4312yes—
189C2×C4⋊C4C22×D4311yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—22no—
193C2×C42C22⋊D4311yescharacteristic
194#107—1722no—
195#104—1722no—
196#102—1722no—
197C22⋊C8—862no—
198#95—22no—
199#95—22no—
200#95C22⋊D4312yes—
201C24—21no—
202#41—1721no—
203#41—1721no—
204#41—1721no—
205#41—1721no—
206C2×Q8—861no—
207C2×D4—21no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—862no—
211C2×D4—861no—
212C2×D4—1721no—
213C2×D4#1062188212yes—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—81no—
219C22×C4—81no—
220C22×C4—1721no—
221C22×C4C2×C22⋊D4311yescharacteristic
222C22×C4C2×C22⋊D4312yes—
223SD16—1724no—
224D8—1724no—
225M16—862no—
226M16—1721no—
227C2×C8—1722no—
228C2×C8—1721no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—81no—
235C4⋊C4—862no—
236C22⋊C4—44no—
237C22⋊C4—42no—
238C22⋊C4—44no—
239C22⋊C4—1722no—
240C42—41no—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—41no—
245C23—41no—
246C23—1721no—
247C23#1306329411yescharacteristic
248Q8—1721no—
249Q8—1721no—
250D4—42no—
251D4—81no—
252D4—3442no—
253D4—3441no—
254D4—3441no—
255D4—1721no—
256D4—1721no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—84no—
271C2×C4—3441no—
272C2×C4—3441no—
273C2×C4—1721no—
274C2×C4C2×#1062188211yescharacteristic
275C2×C4#1306335111yescharacteristic
276C8—3442no—
277C8—1722no—
278C22—21no—
279C22—21no—
280C22—44no—
281C22—42no—
282C22—82no—
283C22—81no—
284C22—81no—
285C22—3441no—
286C22—3441no—
287C22—3441no—
288C22#1458303311yescharacteristic
289C22#1458306711yescharacteristic
290C22#1458308611yescharacteristic
291C4—21no—
292C4—21no—
293C4—42no—
294C4—42no—
295C4—82no—
296C4—82no—
297C4—3441no—
298C2—21no—
299C2—21no—
300C2—82no—
301C2—6881no—
302C2#1913351311yescharacteristic
303C2#1913659111yescharacteristic
304C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2724C2
socleC22×C43B(4,𝔽2)
prime radical#19135636C2
hypercenter#2724D43
hypocenterC43#12097
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2724

Complements

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

NH ≅ G/Ntype
2. #19133597C2semidirect
3. #19132601C2semidirect
4. #19132527C2semidirect
5. C43×#2724C2semidirect
146. #2724D43semidirect
171. C43#12097semidirect

Maximal subgroups

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

subgroupindex
#191356362
#191335972
#191326012
#191325272
C43×#27242
#1209743