Finite Group Databasebeta

← #25009406

Subgroups — #25009406

Order 11008.

456 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 59 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#19142859C211yesmaximal, characteristic
2#19135759C211yesmaximal, characteristic
3#19133622C212yesmaximal, complemented
4#19132620C212yesmaximal, complemented
5C43×#1316C211yesmaximal, characteristic
6#14583525C2211yescharacteristic
7#14583235—22no—
8#14582835—21no—
9#14582835C2212yes—
10#14582822—22no—
11#14582822—22no—
12#14582755—21no—
13#14582755—21no—
14#14582666C2211yescharacteristic
15#14582665—21no—
16#14582637—22no—
17C43×#379C2211yescharacteristic
18C43×#323C2212yes—
19#13063304—22no—
20#13063302—42no—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43D412yes—
23C2×Dic43⋊C4—22no—
24C2×Dic43⋊C4—22no—
25C2×C22⋊Dic43—21no—
26C2×C22⋊Dic43—21no—
27C2×C22⋊Dic43—21no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—42no—
32#13063259—42no—
33#13063250—42no—
34C43⋊#95—21no—
35C43⋊#95D412yes—
36C25×C43D411yescharacteristic
37C2×C22⋊C4×C43—22no—
38C2×C22⋊C4×C43D411yescharacteristic
39C2×C22⋊C4×C43C2311yescharacteristic
40C22⋊C8×C43—22no—
41C24×C43—21no—
42C24×C43—21no—
43C24×C43—41no—
44C24×C43—41no—
45C24×C43—82no—
46C24×C43Q1612yes—
47C24×C43C2×D411yescharacteristic
48C22×C4×C43—21no—
49C22×C4×C43C2×D412yes—
50C22×Dic43—22no—
51C22×Dic43—22no—
52C22×Dic43—22no—
53C22×Dic43—41no—
54C2×Dic86—22no—
55C2×C8×C43—42no—
56C22⋊C4×C43—41no—
57C22⋊C4×C43—41no—
58C22⋊C4×C43—82no—
59C22⋊Dic43—41no—
60C22⋊Dic43—41no—
61C22⋊Dic43—41no—
62C22⋊Dic43—41no—
63C22⋊Dic43—82no—
64C22⋊Dic43—82no—
65C22⋊Dic43—81no—
66C22⋊Dic43—81no—
67C22⋊Dic43—84no—
68C4⋊Dic43—22no—
69C4⋊Dic43—42no—
70C4⋊Dic43—81no—
71Dic43⋊C4—42no—
72Dic43⋊C4—82no—
73Dic43⋊C4—82no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43—22no—
77C23×C43—42no—
78C23×C43—42no—
79C23×C43—42no—
80C23×C43—42no—
81C23×C43—44no—
82C23×C43—41no—
83C23×C43—41no—
84C23×C43—81no—
85C23×C43—82no—
86C23×C43—82no—
87C23×C43—82no—
88C23×C43—84no—
89C23×C43#12011yescharacteristic
90C23×C43C2×Q1611yescharacteristic
91C23×C43#13711yescharacteristic
92C2×C4×C43—22no—
93C2×C4×C43—42no—
94C2×C4×C43—42no—
95C2×C4×C43—41no—
96C2×Dic43—42no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—42no—
101C2×Dic43—42no—
102C2×Dic43—42no—
103C2×Dic43—82no—
104C2×Dic43—81no—
105C2×Dic43—82no—
106Dic86—82no—
107C8×C43—82no—
108#12218—431nomaximal, Sylow
109C22×C43—22no—
110C22×C43—21no—
111C22×C43—21no—
112C22×C43—41no—
113C22×C43—41no—
114C22×C43—42no—
115C22×C43—42no—
116C22×C43—42no—
117C22×C43—44no—
118C22×C43—42no—
119C22×C43—81no—
120C22×C43—82no—
121C22×C43—82no—
122C22×C43—84no—
123C22×C43—82no—
124C22×C43#45111yescharacteristic
125C22×C43#45511yescharacteristic
126C22×C43B(4,𝔽2)11yescharacteristic
127C4×C43—42no—
128C4×C43—81no—
129Dic43—82no—
130Dic43—82no—
131Dic43—82no—
132Dic43—161no—
133#2842—431no—
134#2029—431no—
135#1614—432no—
136#1352—432no—
137#1316D4311yescharacteristic
138C2×C43—21no—
139C2×C43—21no—
140C2×C43—41no—
141C2×C43—41no—
142C2×C43—82no—
143C2×C43#160211yescharacteristic
144C2×C43#220012yes—
145#543—431no—
146#484—862no—
147#399—432no—
148#399—861no—
149#396—862no—
150#396—862no—
151#379—861no—
152#379—861no—
153#379C2×D4311yescharacteristic
154#342—431no—
155#342—861no—
156#328—862no—
157#323C2×D4312yes—
158C43#1221811yescharacteristic, complemented, Sylow
159C25D17211yescharacteristic
160C22⋊Q8—862no—
161C22⋊Q8—1722no—
162C2×C4⋊C4—432no—
163C2×C4⋊C4—862no—
164C2×C4⋊C4—861no—
165C2×C4⋊C4—862no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—861no—
168C2×C22⋊C4—862no—
169C2×C22⋊C4—861no—
170C2×C22⋊C4—862no—
171C2×C22⋊C4—861no—
172C2×C22⋊C4—861no—
173C2×C22⋊C4—1722no—
174C2×C22⋊C4D17211yescharacteristic
175C2×C22⋊C4C22×D4311yescharacteristic
176#107—1722no—
177#103—1722no—
178C22⋊C8—22no—
179#95—432no—
180#95—861no—
181C24—21no—
182C24—21no—
183C24—41no—
184C24—41no—
185C24—82no—
186C24Dic17212yes—
187C24C2×D17211yescharacteristic
188C2×Q8—862no—
189C22×C4—21no—
190C22×C4—862no—
191C22×C4—862no—
192C22×C4—862no—
193C22×C4—1721no—
194C22×C4D4×D4312yes—
195C2×C8—42no—
196C4⋊C4—862no—
197C4⋊C4—3442no—
198C4⋊C4—3442no—
199C4⋊C4—3441no—
200C4⋊C4—1722no—
201C4⋊C4—1722no—
202C22⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4—82no—
205C22⋊C4—3444no—
206C22⋊C4—3442no—
207C22⋊C4—3442no—
208C22⋊C4—3441no—
209C22⋊C4—3441no—
210C22⋊C4—1721no—
211C22⋊C4—1721no—
212C22⋊C4—1721no—
213C22⋊C4—1721no—
214C23—21no—
215C23—21no—
216C23—22no—
217C23—42no—
218C23—42no—
219C23—42no—
220C23—42no—
221C23—44no—
222C23—41no—
223C23—41no—
224C23—81no—
225C23—82no—
226C23—82no—
227C23—82no—
228C23—84no—
229C23#1306329511yescharacteristic
230C23C2×Dic17211yescharacteristic
231C23#1306335811yescharacteristic
232Q8—3442no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—3442no—
238C2×C4—3441no—
239C2×C4—3442no—
240C2×C4—1722no—
241C2×C4—1722no—
242C2×C4—1722no—
243C2×C4—1722no—
244C2×C4—1722no—
245C2×C4—1722no—
246C2×C4—1722no—
247C8—82no—
248C22—22no—
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—42no—
254C22—42no—
255C22—42no—
256C22—44no—
257C22—42no—
258C22—81no—
259C22—82no—
260C22—82no—
261C22—84no—
262C22—82no—
263C22#1458305711yescharacteristic
264C22#1458307911yescharacteristic
265C22#1458308711yescharacteristic
266C4—42no—
267C4—81no—
268C4—3442no—
269C4—3442no—
270C4—3442no—
271C4—6881no—
272C2—21no—
273C2—21no—
274C2—41no—
275C2—41no—
276C2—82no—
277C2#1913355411yescharacteristic
278C2#1913660412yes—
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1316C2
socleC22×C43B(4,𝔽2)
prime radicalC25×C43D4
hypercenter#1316D43
hypocenterC43#12218
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1316

Complements

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

NH ≅ G/Ntype
3. #19133622C2semidirect
4. #19132620C2semidirect
158. C43#12218semidirect

Maximal subgroups

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

subgroupindex
#191428592
#191357592
#191336222
#191326202
C43×#13162
#1221843