Finite Group Databasebeta

← #25006249

Subgroups — #25006249

Order 11008.

480 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 87 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#19139548C211yesmaximal, characteristic
2#19132913C211yesmaximal, characteristic
3#19132540C214yesmaximal, complemented
4C43×#1465C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic
6C2×#13063304—21no—
7C2×#13063304—21no—
8C2×C22⋊(C43⋊C8)—21no—
9#14582835—21no—
10#14582835—21no—
11#14582802C412yes—
12#14582768C2212yes—
13C4×C4⋊Dic43C411yescharacteristic
14#14582625C2212yes—
15#14582623—21no—
16C2×C4×D4×C43C2211yescharacteristic
17C43×#407—21no—
18C43×#324C2212yes—
19C43×#323—21no—
20C22×Dic86—21no—
21C22×C43⋊C8—41no—
22#13063325—41no—
23#13063325—41no—
24#13063304—44no—
25#13063304—44no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43C2×C412yes—
29C2×Dic43⋊C4—22no—
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—22no—
33C2×C4×Dic43C2×C412yes—
34C22⋊(C43⋊C8)—22no—
35C22⋊(C43⋊C8)—41no—
36C43⋊#95—21no—
37C22×D4×C43C2×C411yescharacteristic
38C23×C4×C43D411yescharacteristic
39C23×C4×C43D411yescharacteristic
40C2×M16×C43—41no—
41C4×D4×C43—41no—
42C4×D4×C43—41no—
43C2×C4⋊C4×C43C2311yescharacteristic
44C2×C22⋊C4×C43D411yescharacteristic
45C2×C22⋊C4×C43D411yescharacteristic
46C2×C42×C43C2×C411yescharacteristic
47C22⋊C8×C43—22no—
48C22⋊C8×C43—41no—
49C24×C43C22⋊C411yescharacteristic
50C24×C43C22⋊C411yescharacteristic
51C2×D4×C43—22no—
52C2×D4×C43—22no—
53C2×D4×C43—41no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—42no—
59C22×C4×C43—42no—
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—22no—
66C22×Dic43—22no—
67C2×Dic86—42no—
68C2×Dic86—42no—
69C2×Dic86—41no—
70C2×Dic86—41no—
71M16×C43—82no—
72C2×C8×C43—42no—
73C4⋊C4×C43—41no—
74C22⋊C4×C43—41no—
75C22⋊C4×C43—41no—
76C42×C43—21no—
77C42×C43—21no—
78C22⋊Dic43—44no—
79C22⋊Dic43—44no—
80C4⋊Dic43—24no—
81C4⋊Dic43—42no—
82C4⋊Dic43—42no—
83Dic43⋊C4—44no—
84Dic43⋊C4—44no—
85C4×Dic43—24no—
86C2×C43⋊C8—42no—
87C2×C43⋊C8—82no—
88C23×C43—21no—
89C23×C43—21no—
90C23×C43—21no—
91C23×C43—21no—
92C23×C43—21no—
93C23×C43—41no—
94C23×C43—41no—
95C23×C43—41no—
96C23×C43—41no—
97C23×C43#10112yes—
98C23×C43C2×C22⋊C411yescharacteristic
99D4×C43—44no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—81no—
112C2×C4×C43—81no—
113C2×C4×C43#9911yescharacteristic
114C2×C4×C43#9911yescharacteristic
115C2×C4×C43#13112yes—
116C2×Dic43—24no—
117C2×Dic43—42no—
118C2×Dic43—42no—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122Dic86—82no—
123Dic86—82no—
124C8×C43—82no—
125C43⋊C8—82no—
126#11570—431nomaximal, Sylow
127C22×C43—21no—
128C22×C43—21no—
129C22×C43—22no—
130C22×C43—42no—
131C22×C43—42no—
132C22×C43—41no—
133C22×C43—41no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—41no—
137C22×C43—81no—
138C22×C43—81no—
139C22×C43#40811yescharacteristic
140C22×C43C2×#9911yescharacteristic
141C22×C43C2×#10111yescharacteristic
142C4×C43—21no—
143C4×C43—22no—
144C4×C43—41no—
145C4×C43—41no—
146C4×C43—41no—
147C4×C43#35312yes—
148Dic43—44no—
149Dic43—82no—
150#2542—431no—
151#1465D4311yescharacteristic
152#1459—431no—
153#1325—434no—
154C2×C43—21no—
155C2×C43—21no—
156C2×C43—42no—
157C2×C43—81no—
158C2×C43#147211yescharacteristic
159C2×C43C2×#35311yescharacteristic
160C2×C43#213511yescharacteristic
161C2×C4⋊Q8—431no—
162C2×C22⋊Q8—861no—
163C2×C22⋊Q8—861no—
164C2×C4×D4C2×D4311yescharacteristic
165#407—21no—
166C2×C22⋊C8—861no—
167#399—861no—
168#399—861no—
169#390—432no—
170#384—432no—
171C4×C4⋊C4—431no—
172#324—432no—
173#324C2×D4312yes—
174#323—21no—
175#323—861no—
176C43#1157011yescharacteristic, complemented, Sylow
177C22×Q8—861no—
178C22×D4C4×D4311yescharacteristic
179C23×C4D17211yescharacteristic
180C23×C4C22⋊D4311yescharacteristic
181C2×M16—41no—
182C22×C8—1721no—
183C4⋊Q8—1721no—
184C4⋊Q8—1721no—
185C22⋊Q8—1724no—
186C22⋊Q8—1724no—
187C4×D4—41no—
188C4×D4—41no—
189C2×C4⋊C4—432no—
190C2×C4⋊C4—861no—
191C2×C4⋊C4—861no—
192C2×C4⋊C4—862no—
193C2×C4⋊C4—862no—
194C2×C4⋊C4C22×D4311yescharacteristic
195C2×C22⋊C4—862no—
196C2×C22⋊C4—862no—
197C2×C22⋊C4D17211yescharacteristic
198C2×C22⋊C4C22⋊D4311yescharacteristic
199C2×C42—432no—
200C2×C42C4×D4311yescharacteristic
201C22⋊C8—22no—
202C22⋊C8—41no—
203C22⋊C8—862no—
204C22⋊C8—1721no—
205#95—861no—
206C24(C2×D43)⋊C411yescharacteristic
207C24(C2×D43)⋊C411yescharacteristic
208C2×Q8—1722no—
209C2×Q8—1722no—
210C2×Q8—1721no—
211C2×Q8—1721no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—41no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—862no—
222C22×C4—862no—
223C22×C4(C2×D43)⋊C411yescharacteristic
224C22×C4(C2×D43)⋊C411yescharacteristic
225C22×C4C2×C4×D4311yescharacteristic
226C22×C4C2×D17211yescharacteristic
227C22×C4C2×C22⋊D4311yescharacteristic
228M16—82no—
229C2×C8—42no—
230C2×C8—3442no—
231C2×C8—1722no—
232C4⋊C4—41no—
233C4⋊C4—864no—
234C4⋊C4—1722no—
235C4⋊C4—1722no—
236C4⋊C4—1724no—
237C4⋊C4—1724no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—1724no—
241C22⋊C4—1724no—
242C42—21no—
243C42—21no—
244C42—864no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23#1306324312yes—
255C23C2×(C2×D43)⋊C411yescharacteristic
256Q8—3442no—
257Q8—3442no—
258D4—44no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—864no—
273C2×C4—1722no—
274C2×C4—1722no—
275C2×C4—1722no—
276C2×C4—1722no—
277C2×C4—1722no—
278C2×C4#1306323911yescharacteristic
279C2×C4#1306323911yescharacteristic
280C2×C4#1306333312yes—
281C8—82no—
282C8—3442no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22—81no—
295C22#1458286711yescharacteristic
296C22C2×#1306323911yescharacteristic
297C22C2×#1306324311yescharacteristic
298C4—22no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—3442no—
304C4—1724no—
305C4#1458269112yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2#1913296011yescharacteristic
311C2C2×#1458269111yescharacteristic
312C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1465C2
socleC22×C43C2×#99
prime radicalC22×D4×C43C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1465D43
hypocenterC43#11570
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #19132540C2semidirect
176. C43#11570semidirect

Maximal subgroups

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

subgroupindex
#191395482
#191329132
#191325402
C43×#14652
#1157043