Finite Group Databasebeta

← #25007282

Subgroups — #25007282

Order 11008.

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

normal subgroups only

This group has 478 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
1C2×#14582829C211yesmaximal, characteristic
2#19132925C211yesmaximal, characteristic
3#19132600C214yesmaximal, complemented
4C43×#1821C211yesmaximal, characteristic
5C22×C4⋊Dic43C411yescharacteristic
6C22×Dic43⋊C4—21no—
7#14582863—21no—
8#14582829—21no—
9#14582829—21no—
10#14582829C412yes—
11#14582829C2212yes—
12C2×C43⋊#95—21no—
13C2×C43⋊#95C411yescharacteristic
14#14582625—21no—
15#14582625C2212yes—
16C22×C4⋊C4×C43C2211yescharacteristic
17C43×#407—21no—
18C43×#343—21no—
19C43×#343C2212yes—
20C23×Dic43—21no—
21C23×Dic43—21no—
22C2×#10621877—41no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—41no—
25C2×C4⋊Dic43—41no—
26C2×C4⋊Dic43C2×C412yes—
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—44no—
30C22⋊(C43⋊C8)—22no—
31C22⋊(C43⋊C8)—41no—
32C43⋊#95—21no—
33C43⋊#95—22no—
34C43⋊#95—22no—
35C43⋊#95C2×C412yes—
36C23×C4×C43C2×C411yescharacteristic
37C23×C4×C43D411yescharacteristic
38C23×C4×C43D411yescharacteristic
39C2×M16×C43—22no—
40C2×C4⋊C4×C43—41no—
41C2×C4⋊C4×C43—41no—
42C2×C4⋊C4×C43C2×C411yescharacteristic
43C2×C4⋊C4×C43D411yescharacteristic
44C2×C4⋊C4×C43D411yescharacteristic
45C2×C4⋊C4×C43C2311yescharacteristic
46C22⋊C8×C43—41no—
47C22⋊C8×C43—41no—
48C24×C43C22⋊C411yescharacteristic
49C22×C4×C43—22no—
50C22×C4×C43—21no—
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—41no—
57C22×C4×C43—42no—
58C22×C4×C43—42no—
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—24no—
66C22×Dic43—22no—
67C22×Dic43—22no—
68C22×Dic43—42no—
69C22×Dic43—42no—
70C22×Dic43—42no—
71C22×Dic43—42no—
72C22×Dic43—41no—
73C22×Dic43—41no—
74M16×C43—42no—
75M16×C43—42no—
76C2×C8×C43—42no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊Dic43—42no—
82C4⋊Dic43—42no—
83Dic43⋊C4—44no—
84Dic43⋊C4—44no—
85#10621877—82no—
86C2×C43⋊C8—42no—
87C23×C43—22no—
88C23×C43—22no—
89C23×C43—21no—
90C23×C43—21no—
91C23×C43#9911yescharacteristic
92C23×C43#9911yescharacteristic
93C23×C43C2×C22⋊C411yescharacteristic
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—81no—
113C2×C4×C43AGL(1,ℤ/8)12yes—
114C2×Dic43—24no—
115C2×Dic43—48no—
116C2×Dic43—42no—
117C2×Dic43—42no—
118C2×Dic43—42no—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—82no—
122C2×Dic43—82no—
123C8×C43—82no—
124C43⋊C8—82no—
125#11803—431nomaximal, Sylow
126C22×C43—24no—
127C22×C43—24no—
128C22×C43—21no—
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—21no—
133C22×C43—21no—
134C22×C43#35212yes—
135C22×C43#35612yes—
136C22×C43C2×#9911yescharacteristic
137C22×C43#41811yescharacteristic
138C22×C43#42111yescharacteristic
139C4×C43—22no—
140C4×C43—41no—
141C4×C43—41no—
142C4×C43—41no—
143C4×C43—41no—
144C4×C43—41no—
145Dic43—44no—
146Dic43—82no—
147C2×#398—431no—
148#1821D4311yescharacteristic
149#1463—431no—
150#1346—434no—
151C2×C43—21no—
152C2×C43—22no—
153C2×C43—22no—
154C2×C43—21no—
155C2×C43#151011yescharacteristic
156C2×C43C2×#35211yescharacteristic
157C2×C43C2×#35611yescharacteristic
158C22×C4⋊C4—431no—
159C22×C4⋊C4—861no—
160C22×C4⋊C4C2×D4311yescharacteristic
161#407—21no—
162#407—861no—
163#398—432no—
164#398—432no—
165#398—861no—
166#398—861no—
167C2×#95—431no—
168C2×#95—861no—
169#343—21no—
170#343C2×D4312yes—
171#324—432no—
172#324—861no—
173C43#1180311yescharacteristic, complemented, Sylow
174C23×C4—861no—
175C23×C4—861no—
176C23×C4C4×D4311yescharacteristic
177C23×C4D17211yescharacteristic
178C23×C4C22⋊D4311yescharacteristic
179C2×M16—22no—
180C2×M16—1721no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—432no—
184C2×C4⋊C4—861no—
185C2×C4⋊C4—862no—
186C2×C4⋊C4—862no—
187C2×C4⋊C4—1721no—
188C2×C4⋊C4—1721no—
189C2×C4⋊C4—1724no—
190C2×C4⋊C4C4×D4311yescharacteristic
191C2×C4⋊C4D17211yescharacteristic
192C2×C4⋊C4C22⋊D4311yescharacteristic
193C2×C4⋊C4C22×D4311yescharacteristic
194C22⋊C8—41no—
195C22⋊C8—41no—
196C22⋊C8—862no—
197C22⋊C8—1721no—
198#95—432no—
199#95—861no—
200#95—862no—
201#95—862no—
202C24(C2×D43)⋊C411yescharacteristic
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—41no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—864no—
214C22×C4—862no—
215C22×C4—862no—
216C22×C4—1722no—
217C22×C4—1722no—
218C22×C4—1721no—
219C22×C4—1721no—
220C22×C4—1722no—
221C22×C4—1722no—
222C22×C4(C2×D43)⋊C411yescharacteristic
223C22×C4(C2×D43)⋊C411yescharacteristic
224C22×C4(C2×D43)⋊C411yescharacteristic
225C22×C4C2×C4×D4311yescharacteristic
226C22×C4C2×D17211yescharacteristic
227C22×C4C2×C22⋊D4311yescharacteristic
228M16—42no—
229M16—42no—
230M16—3442no—
231C2×C8—42no—
232C2×C8—1722no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—1722no—
238C4⋊C4—1724no—
239C4⋊C4—1722no—
240C4⋊C4—1724no—
241C23—21no—
242C23—21no—
243C23—22no—
244C23—22no—
245C23#1306323911yescharacteristic
246C23#1306323911yescharacteristic
247C23C2×(C2×D43)⋊C411yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—864no—
268C2×C4—3442no—
269C2×C4—3442no—
270C2×C4—1722no—
271C2×C4—1722no—
272C2×C4—1722no—
273C2×C4—1728no—
274C2×C4—1722no—
275C2×C4—1722no—
276C2×C4#1306335012yes—
277C8—82no—
278C8—3442no—
279C22—24no—
280C22—24no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22#1458269012yes—
288C22#1458269712yes—
289C22C2×#1306323911yescharacteristic
290C22#1458290311yescharacteristic
291C22#1458291711yescharacteristic
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—3442no—
299C4—1724no—
300C2—21no—
301C2—21no—
302C2—22no—
303C2—22no—
304C2#1913312311yescharacteristic
305C2C2×#1458269011yescharacteristic
306C2C2×#1458269711yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1821C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1821D43
hypocenterC43#11803
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #19132600C2semidirect
173. C43#11803semidirect

Maximal subgroups

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

subgroupindex
C2×#145828292
#191329252
#191326002
C43×#18212
#1180343