Finite Group Databasebeta

← #25007352

Subgroups — #25007352

Order 11008.

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

normal subgroups only

This group has 368 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#19140416C211yesmaximal, characteristic
2#19132929C211yesmaximal, characteristic
3#19132624C214yesmaximal, complemented
4C43×#1822C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic
6#14582956—21no—
7#14582838—21no—
8#14582835—21no—
9#14582819C2212yes—
10#14582811C412yes—
11#14582797—21no—
12#14582765C411yescharacteristic
13#14582759—21no—
14#14582625C2212yes—
15#14582623—21no—
16C2×#117×C43C2211yescharacteristic
17C43×#407—21no—
18C43×#343—21no—
19C43×#343C2212yes—
20C22×Dic86C2×C412yes—
21#13063325—41no—
22#13063325—41no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—21no—
26C2×Dic43⋊C4—22no—
27C2×C22⋊Dic43—22no—
28C4⋊(C43⋊C8)—41no—
29C22⋊(C43⋊C8)—22no—
30#13063236—41no—
31C43⋊#95—22no—
32C43⋊#95—21no—
33C43⋊#95—22no—
34C43⋊#95C2×C412yes—
35C23×C4×C43D411yescharacteristic
36C2×M16×C43—22no—
37#117×C43—41no—
38#117×C43—41no—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C4⋊C4×C43C2311yescharacteristic
41C2×C22⋊C4×C43C2×C411yescharacteristic
42C2×C22⋊C4×C43D411yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C22⋊C8×C43—41no—
46C22⋊C8×C43—41no—
47C24×C43C22⋊C411yescharacteristic
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43—22no—
51C22×C4×C43—41no—
52C22×C4×C43C22⋊C411yescharacteristic
53C22×C4×C43C22⋊C411yescharacteristic
54C22×C4×C43C22⋊C411yescharacteristic
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×Dic43—22no—
59C22×Dic43—22no—
60C2×Dic86—42no—
61C2×Dic86—82no—
62M16×C43—42no—
63M16×C43—42no—
64C2×C8×C43—42no—
65C4⋊C4×C43—41no—
66C4⋊C4×C43—41no—
67C22⋊C4×C43—41no—
68C22⋊C4×C43—41no—
69C42×C43—21no—
70C42×C43—21no—
71C42×C43—21no—
72C42×C43—21no—
73C22⋊Dic43—82no—
74C4⋊Dic43—42no—
75C4⋊Dic43—42no—
76C4⋊Dic43—41no—
77C4⋊Dic43—41no—
78Dic43⋊C4—82no—
79C2×C43⋊C8—42no—
80C23×C43—21no—
81C23×C43—21no—
82C23×C43—21no—
83C23×C43—41no—
84C23×C43—41no—
85C23×C43C2×C22⋊C411yescharacteristic
86C2×C4×C43—21no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—41no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43#9911yescharacteristic
101C2×C4×C43#9911yescharacteristic
102C2×C4×C43#13712yes—
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109Dic86—84no—
110C8×C43—82no—
111C43⋊C8—82no—
112#11819—431nomaximal, Sylow
113C22×C43—21no—
114C22×C43—21no—
115C22×C43—42no—
116C22×C43—41no—
117C22×C43—41no—
118C22×C43—41no—
119C22×C43—81no—
120C22×C43C2×#9911yescharacteristic
121C22×C43#41911yescharacteristic
122C22×C43#42111yescharacteristic
123C4×C43—22no—
124C4×C43—21no—
125C4×C43—21no—
126C4×C43—41no—
127C4×C43—41no—
128C4×C43—41no—
129C4×C43—41no—
130Dic43—82no—
131Dic43—82no—
132#2628—431no—
133#1822D4311yescharacteristic
134#1464—431no—
135#1354—434no—
136C2×C43—21no—
137C2×C43—21no—
138C2×C43—81no—
139C2×C43#151111yescharacteristic
140C2×C43#212211yescharacteristic
141C2×C43#213511yescharacteristic
142C2×C4⋊Q8—431no—
143C2×#117C2×D4311yescharacteristic
144#432—861no—
145#407—21no—
146#400—861no—
147#399—861no—
148#395—432no—
149#393—432no—
150#389—861no—
151#382—431no—
152#380—861no—
153#343—21no—
154#343C2×D4312yes—
155#324—432no—
156#323—861no—
157C43#1181911yescharacteristic, complemented, Sylow
158C22×Q8—432no—
159C23×C4C22⋊D4311yescharacteristic
160C2×M16—22no—
161C4⋊Q8—1721no—
162C4⋊Q8—1721no—
163#117—41no—
164#117—41no—
165C2×C4⋊C4—862no—
166C2×C4⋊C4—861no—
167C2×C4⋊C4—861no—
168C2×C4⋊C4—861no—
169C2×C4⋊C4C22⋊D4311yescharacteristic
170C2×C4⋊C4C22×D4311yescharacteristic
171C2×C22⋊C4—862no—
172C2×C22⋊C4C4×D4311yescharacteristic
173C2×C22⋊C4D17211yescharacteristic
174C2×C42C4×D4311yescharacteristic
175C2×C42D17211yescharacteristic
176C4⋊C8—1721no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179C22⋊C8—862no—
180#97—1721no—
181#95—432no—
182#95—861no—
183#95—862no—
184#95—862no—
185C24(C2×D43)⋊C411yescharacteristic
186C2×Q8—3442no—
187C2×Q8—1722no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—41no—
192C22×C4—862no—
193C22×C4—862no—
194C22×C4(C2×D43)⋊C411yescharacteristic
195C22×C4(C2×D43)⋊C411yescharacteristic
196C22×C4(C2×D43)⋊C411yescharacteristic
197C22×C4C2×C4×D4311yescharacteristic
198C22×C4C2×D17211yescharacteristic
199C22×C4C2×C22⋊D4311yescharacteristic
200M16—42no—
201M16—42no—
202C2×C8—42no—
203C2×C8—1722no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—3442no—
207C4⋊C4—1722no—
208C4⋊C4—1722no—
209C4⋊C4—1721no—
210C4⋊C4—1721no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—3442no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×(C2×D43)⋊C411yescharacteristic
224Q8—3444no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—1722no—
240C2×C4—1722no—
241C2×C4—1722no—
242C2×C4—1722no—
243C2×C4—1722no—
244C2×C4—1722no—
245C2×C4#1306323911yescharacteristic
246C2×C4#1306323911yescharacteristic
247C2×C4#1306335512yes—
248C8—82no—
249C8—3442no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#1306323911yescharacteristic
258C22#1458290711yescharacteristic
259C22#1458291711yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—3442no—
268C4—3442no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#1913312711yescharacteristic
273C2#1913624611yescharacteristic
274C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1822C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1822D43
hypocenterC43#11819
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1822

Complements

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

NH ≅ G/Ntype
3. #19132624C2semidirect
157. C43#11819semidirect

Maximal subgroups

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

subgroupindex
#191404162
#191329292
#191326242
C43×#18222
#1181943