Finite Group Databasebeta

← #25006915

Subgroups — #25006915

Order 11008.

432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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#19132909C211yesmaximal, characteristic
3#19132624C214yesmaximal, complemented
4C43×#1742C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic
6#14582952—21no—
7#14582838—21no—
8#14582835—21no—
9#14582819C2212yes—
10#14582811C412yes—
11#14582797—21no—
12#14582765C411yescharacteristic
13#14582759—21no—
14#14582625C2212yes—
15#14582623—21no—
16C22×M16×C43—21no—
17C2×#117×C43C2211yescharacteristic
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—
30C4×C43⋊C8—41no—
31C43⋊#95—22no—
32C43⋊#95—21no—
33C43⋊#95—22no—
34C43⋊#95C2×C412yes—
35C23×C4×C43D411yescharacteristic
36C2×M16×C43—24no—
37C2×M16×C43—22no—
38C2×M16×C43—41no—
39C2×M16×C43—42no—
40C22×C8×C43—41no—
41#117×C43—41no—
42#117×C43—41no—
43C2×C4⋊C4×C43D411yescharacteristic
44C2×C4⋊C4×C43C2311yescharacteristic
45C2×C22⋊C4×C43C2×C411yescharacteristic
46C2×C22⋊C4×C43D411yescharacteristic
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C24×C43C22⋊C411yescharacteristic
50C22×C4×C43—21no—
51C22×C4×C43—21no—
52C22×C4×C43—22no—
53C22×C4×C43C22⋊C411yescharacteristic
54C22×C4×C43C22⋊C411yescharacteristic
55C22×C4×C43C22⋊C411yescharacteristic
56C22×C4×C43SD1612yes—
57C22×C4×C43Q1612yes—
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—22no—
62C22×Dic43—22no—
63C2×Dic86—42no—
64C2×Dic86—82no—
65M16×C43—24no—
66M16×C43—44no—
67M16×C43—42no—
68C2×C8×C43—42no—
69C2×C8×C43—44no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—41no—
72C22⋊C4×C43—41no—
73C22⋊C4×C43—41no—
74C42×C43—21no—
75C42×C43—21no—
76C42×C43—21no—
77C42×C43—21no—
78C22⋊Dic43—82no—
79C4⋊Dic43—42no—
80C4⋊Dic43—41no—
81C4⋊Dic43—41no—
82C4⋊Dic43—42no—
83Dic43⋊C4—82no—
84C2×C43⋊C8—42no—
85C23×C43—21no—
86C23×C43—21no—
87C23×C43—41no—
88C23×C43—41no—
89C23×C43#10312yes—
90C23×C43C2×C22⋊C411yescharacteristic
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43#9911yescharacteristic
106C2×C4×C43#9911yescharacteristic
107C2×C4×C43#10312yes—
108C2×C4×C43#10412yes—
109C2×C4×C43C2×SD1611yescharacteristic
110C2×C4×C43C2×Q1611yescharacteristic
111C2×Dic43—42no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115C2×Dic43—42no—
116C2×Dic43—42no—
117Dic86—84no—
118C8×C43—44no—
119C43⋊C8—82no—
120#11724—431nomaximal, Sylow
121C22×C43—21no—
122C22×C43—21no—
123C22×C43—22no—
124C22×C43—42no—
125C22×C43—41no—
126C22×C43—41no—
127C22×C43—81no—
128C22×C43C2×#9911yescharacteristic
129C22×C43C2×#10311yescharacteristic
130C22×C43C2×#10411yescharacteristic
131C4×C43—21no—
132C4×C43—21no—
133C4×C43—41no—
134C4×C43—41no—
135C4×C43—41no—
136C4×C43—41no—
137C4×C43#32812yes—
138C4×C43#32812yes—
139Dic43—82no—
140Dic43—82no—
141#2628—431no—
142#1742D4311yescharacteristic
143#1458—431no—
144#1354—434no—
145C2×C43—21no—
146C2×C43—21no—
147C2×C43—42no—
148C2×C43C2×#32811yescharacteristic
149C2×C43#212211yescharacteristic
150C2×C43#213511yescharacteristic
151C22×M16—21no—
152C2×C4⋊Q8—431no—
153C2×#117C2×D4311yescharacteristic
154#431—861no—
155#400—861no—
156#399—861no—
157#395—432no—
158#393—432no—
159#389—861no—
160#382—431no—
161#380—861no—
162#343—21no—
163#343C2×D4312yes—
164#324—432no—
165#323—861no—
166C43#1172411yescharacteristic, complemented, Sylow
167C22×Q8—432no—
168C23×C4C22⋊D4311yescharacteristic
169C2×M16—24no—
170C2×M16—22no—
171C2×M16—41no—
172C2×M16—42no—
173C22×C8—41no—
174C4⋊Q8—1721no—
175C4⋊Q8—1721no—
176#117—41no—
177#117—41no—
178C2×C4⋊C4—862no—
179C2×C4⋊C4—861no—
180C2×C4⋊C4—861no—
181C2×C4⋊C4—861no—
182C2×C4⋊C4C22⋊D4311yescharacteristic
183C2×C4⋊C4C22×D4311yescharacteristic
184C2×C22⋊C4—862no—
185C2×C22⋊C4C4×D4311yescharacteristic
186C2×C22⋊C4D17211yescharacteristic
187C2×C42C4×D4311yescharacteristic
188C2×C42D17211yescharacteristic
189C4⋊C8—1721no—
190C22⋊C8—862no—
191C4×C8—1721no—
192#95—432no—
193#95—861no—
194#95—862no—
195#95—862no—
196C24(C2×D43)⋊C411yescharacteristic
197C2×Q8—3442no—
198C2×Q8—1722no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—862no—
203C22×C4—862no—
204C22×C4(C2×D43)⋊C411yescharacteristic
205C22×C4(C2×D43)⋊C411yescharacteristic
206C22×C4(C2×D43)⋊C411yescharacteristic
207C22×C4#1062188312yes—
208C22×C4#1062188512yes—
209C22×C4C2×C4×D4311yescharacteristic
210C22×C4C2×D17211yescharacteristic
211C22×C4C2×C22⋊D4311yescharacteristic
212M16—24no—
213M16—44no—
214M16—42no—
215C2×C8—42no—
216C2×C8—44no—
217C2×C8—1722no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—3442no—
221C4⋊C4—1722no—
222C4⋊C4—1721no—
223C4⋊C4—1721no—
224C4⋊C4—1722no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—3442no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23#1306324812yes—
237C23C2×(C2×D43)⋊C411yescharacteristic
238Q8—3444no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—1722no—
254C2×C4—1722no—
255C2×C4—1722no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4#1306323911yescharacteristic
260C2×C4#1306323911yescharacteristic
261C2×C4#1306324812yes—
262C2×C4#1306325312yes—
263C2×C4C2×#1062188311yescharacteristic
264C2×C4C2×#1062188511yescharacteristic
265C8—44no—
266C8—3442no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22C2×#1306323911yescharacteristic
275C22C2×#1306324811yescharacteristic
276C22C2×#1306325311yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—3442no—
284C4—3442no—
285C4#1458263512yes—
286C4#1458263512yes—
287C2—21no—
288C2—21no—
289C2—42no—
290C2C2×#1458263511yescharacteristic
291C2#1913624611yescharacteristic
292C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1742C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1742D43
hypocenterC43#11724
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
3. #19132624C2semidirect
166. C43#11724semidirect

Maximal subgroups

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

subgroupindex
#191404162
#191329092
#191326242
C43×#17422
#1172443