Finite Group Databasebeta

← #25007237

Subgroups — #25007237

Order 11008.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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#19139957C211yesmaximal, characteristic
2C4×#13063244C211yesmaximal, characteristic
3#19132626C212yesmaximal
4#19132623C212yesmaximal
5C43×#1467C211yesmaximal, characteristic
6C2×C4×Dic86C411yescharacteristic
7C2×#13063244—21no—
8C4×#10621877—21no—
9#14582838C411yescharacteristic
10#14582838C2211yescharacteristic
11#14582819C411yescharacteristic
12#14582819C2211yescharacteristic
13#14582806—21no—
14#14582795—21no—
15#14582783—21no—
16#14582783—21no—
17#14582765C411yescharacteristic
18#14582668C2212yes—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#324—21no—
22C43×#324C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C2×#10621877—22no—
25C4×Dic86—41no—
26C4×Dic86—41no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×C4×Dic43—21no—
33#13063244—24no—
34#13063236—41no—
35C4×C43⋊C8—41no—
36C43⋊#95—21no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C22×Q8×C43D411yescharacteristic
46C4×Q8×C43—41no—
47C4×Q8×C43—41no—
48C2×C4⋊C4×C43C2×C411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C4⋊C8×C43—41no—
55C22⋊C8×C43—22no—
56#97×C43—41no—
57C2×Q8×C43—22no—
58C2×Q8×C43—22no—
59C2×Q8×C43—41no—
60C22×C4×C43C22⋊C411yescharacteristic
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×Dic86—41no—
72C2×Dic86—42no—
73C2×C8×C43—42no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C42×C43—21no—
78C42×C43—21no—
79C42×C43—21no—
80C42×C43—21no—
81C42×C43—21no—
82C42×C43—21no—
83C4⋊Dic43—42no—
84C4⋊Dic43—41no—
85Dic43⋊C4—42no—
86Dic43⋊C4—42no—
87Dic43⋊C4—41no—
88Dic43⋊C4—41no—
89C4×Dic43—42no—
90#10621877—24no—
91#10621877—42no—
92C2×C43⋊C8—42no—
93C23×C43C2×C22⋊C411yescharacteristic
94Q8×C43—44no—
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—21no—
104C2×C4×C43—21no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43#9911yescharacteristic
110C2×C4×C43#9911yescharacteristic
111C2×C4×C43#10412yes—
112C2×C4×C43#13712yes—
113C2×Dic43—22no—
114C2×Dic43—41no—
115C2×Dic43—41no—
116C2×Dic43—41no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—42no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124Dic86—42no—
125Dic86—42no—
126C8×C43—82no—
127C43⋊C8—44no—
128#11792—431nomaximal, Sylow
129C22×C43—21no—
130C22×C43—21no—
131C22×C43C2×#9911yescharacteristic
132C22×C43#41911yescharacteristic
133C22×C43C2×#10411yescharacteristic
134C4×C43—21no—
135C4×C43—21no—
136C4×C43—22no—
137C4×C43—22no—
138C4×C43—41no—
139C4×C43—41no—
140C4×C43—41no—
141C4×C43—41no—
142Dic43—42no—
143Dic43—81no—
144Dic43—81no—
145Dic43—81no—
146#2581—431no—
147C4×#101—431no—
148#1467D4311yescharacteristic
149#1354—432no—
150#1353—432no—
151C2×C43—21no—
152C2×C43—21no—
153C2×C43#150811yescharacteristic
154C2×C43#212011yescharacteristic
155C2×C43#213311yescharacteristic
156C2×C4×Q8—431no—
157C2×C4×Q8C2×D4311yescharacteristic
158#432—21no—
159C2×#101—861no—
160C4×M16—861no—
161#400—431no—
162#400—431no—
163#395—431no—
164#395—431no—
165#391—861no—
166#389—861no—
167#387—861no—
168#387—861no—
169#382—431no—
170#343—432no—
171#324—21no—
172#324C2×D4312yes—
173C43#1179211yescharacteristic, complemented, Sylow
174C22×Q8—431no—
175C22×Q8D17211yescharacteristic
176C2×M16—862no—
177C4×Q8—41no—
178C4×Q8—41no—
179C4×Q8—1721no—
180C4×Q8—1721no—
181C2×C4⋊C4—431no—
182C2×C4⋊C4—861no—
183C2×C4⋊C4—861no—
184C2×C4⋊C4—861no—
185C2×C4⋊C4—861no—
186C2×C4⋊C4C4×D4311yescharacteristic
187C2×C4⋊C4C22⋊D4311yescharacteristic
188C2×C4⋊C4C22×D4311yescharacteristic
189C2×C42—861no—
190C2×C42C4×D4311yescharacteristic
191C2×C42D17211yescharacteristic
192C2×C42C22⋊D4311yescharacteristic
193C4⋊C8—41no—
194#101—864no—
195C22⋊C8—22no—
196#97—41no—
197#97—1721no—
198C4×C8—1721no—
199#95—431no—
200#95—431no—
201#95—861no—
202#95—861no—
203#95—861no—
204#95—861no—
205#95—861no—
206#95—861no—
207#95—861no—
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C2×Q8—1721no—
212C2×Q8—1722no—
213C22×C4—861no—
214C22×C4—861no—
215C22×C4—861no—
216C22×C4—861no—
217C22×C4(C2×D43)⋊C411yescharacteristic
218C22×C4(C2×D43)⋊C411yescharacteristic
219C22×C4(C2×D43)⋊C411yescharacteristic
220C22×C4(C2×D43)⋊C411yescharacteristic
221C22×C4C2×C4×D4311yescharacteristic
222C22×C4C2×D17211yescharacteristic
223C22×C4C2×C22⋊D4311yescharacteristic
224M16—864no—
225M16—1722no—
226C2×C8—42no—
227C2×C8—1722no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—1721no—
232C4⋊C4—1722no—
233C4⋊C4—1722no—
234C4⋊C4—1721no—
235C4⋊C4—1721no—
236C4⋊C4—1722no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—1722no—
244C23C2×(C2×D43)⋊C411yescharacteristic
245Q8—44no—
246Q8—1722no—
247Q8—1722no—
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—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—862no—
263C2×C4—1721no—
264C2×C4—1721no—
265C2×C4—1721no—
266C2×C4—1721no—
267C2×C4—1722no—
268C2×C4—1721no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1721no—
273C2×C4#1306323911yescharacteristic
274C2×C4#1306323911yescharacteristic
275C2×C4#1306325112yes—
276C2×C4#1306335812yes—
277C8—82no—
278C8—1724no—
279C22—21no—
280C22—21no—
281C22C2×#1306323911yescharacteristic
282C22#1458290911yescharacteristic
283C22C2×#1306325111yescharacteristic
284C4—21no—
285C4—21no—
286C4—22no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—3441no—
293C4—3441no—
294C4—3441no—
295C4—1722no—
296C2—21no—
297C2—21no—
298C2#1913311611yescharacteristic
299C2#1913623411yescharacteristic
300C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1467C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1467D43
hypocenterC43#11792
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
173. C43#11792semidirect

Maximal subgroups

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

subgroupindex
#191399572
C4×#130632442
#191326262
#191326232
C43×#14672
#1179243