Finite Group Databasebeta

← #25007434

Subgroups — #25007434

Order 11008.

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

normal subgroups only

This group has 340 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#19140471C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic
3#19132623C212yesmaximal
4#19132602C212yesmaximal
5C43×#1467C211yesmaximal, characteristic
6C2×#13063317C411yescharacteristic
7#14582923—21no—
8C2×#13063244—21no—
9#14582838C411yescharacteristic
10#14582838C2211yescharacteristic
11#14582837—21no—
12#14582829C411yescharacteristic
13#14582829C2211yescharacteristic
14#14582818—21no—
15#14582783—21no—
16#14582783—21no—
17#14582767C411yescharacteristic
18#14582668C2212yes—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#324—21no—
22C43×#324C2212yes—
23C2×#10621877—22no—
24#13063317—41no—
25#13063317—41no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C4⋊(C43⋊C8)—41no—
33C4⋊(C43⋊C8)—41no—
34#13063244—42no—
35C43⋊#95—21no—
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—21no—
58C2×Q8×C43—21no—
59C2×Q8×C43—41no—
60C2×Q8×C43—41no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C2×C8×C43—42no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C42×C43—21no—
77C42×C43—21no—
78C42×C43—21no—
79C42×C43—21no—
80C42×C43—21no—
81C42×C43—21no—
82C4⋊Dic43—41no—
83C4⋊Dic43—41no—
84Dic43⋊C4—42no—
85Dic43⋊C4—42no—
86Dic43⋊C4—41no—
87Dic43⋊C4—41no—
88Dic43⋊C4—41no—
89Dic43⋊C4—41no—
90#10621877—42no—
91#10621877—42no—
92C2×C43⋊C8—42no—
93C23×C43C2×C22⋊C411yescharacteristic
94Q8×C43—42no—
95Q8×C43—42no—
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—21no—
106C2×C4×C43—21no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43#9911yescharacteristic
112C2×C4×C43#9911yescharacteristic
113C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C43#13711yescharacteristic
115C2×Dic43—41no—
116C2×Dic43—41no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—42no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C8×C43—82no—
127C43⋊C8—82no—
128#11835—431nomaximal, Sylow
129C22×C43—21no—
130C22×C43—21no—
131C22×C43C2×#9911yescharacteristic
132C22×C43#41711yescharacteristic
133C22×C43#42111yescharacteristic
134C4×C43—21no—
135C4×C43—21no—
136C4×C43—21no—
137C4×C43—21no—
138C4×C43—41no—
139C4×C43—41no—
140C4×C43—41no—
141C4×C43—41no—
142C4×C43—41no—
143Dic43—81no—
144Dic43—81no—
145Dic43—81no—
146Dic43—81no—
147#2634—431no—
148#1801—431no—
149#1467D4311yescharacteristic
150#1353—432no—
151#1346—432no—
152C2×C43—21no—
153C2×C43—21no—
154C2×C43#151311yescharacteristic
155C2×C43#212311yescharacteristic
156C2×C43#213311yescharacteristic
157C2×#125—431no—
158C2×C4×Q8C2×D4311yescharacteristic
159#432—21no—
160#423—861no—
161C2×#101—861no—
162#400—431no—
163#400—431no—
164#400—861no—
165#398—431no—
166#398—431no—
167#395—861no—
168#387—861no—
169#387—861no—
170#383—431no—
171#343—432no—
172#324—21no—
173#324C2×D4312yes—
174C43#1183511yescharacteristic, complemented, Sylow
175C22×Q8D17211yescharacteristic
176C2×M16—862no—
177#125—1721no—
178#125—1721no—
179C4×Q8—41no—
180C4×Q8—41no—
181C2×C4⋊C4—431no—
182C2×C4⋊C4—431no—
183C2×C4⋊C4—861no—
184C2×C4⋊C4—861no—
185C2×C4⋊C4—861no—
186C2×C4⋊C4—861no—
187C2×C4⋊C4C4×D4311yescharacteristic
188C2×C4⋊C4C22⋊D4311yescharacteristic
189C2×C4⋊C4C22×D4311yescharacteristic
190C2×C42C4×D4311yescharacteristic
191C2×C42D17211yescharacteristic
192C2×C42C22⋊D4311yescharacteristic
193C4⋊C8—41no—
194C4⋊C8—1721no—
195C4⋊C8—1721no—
196#101—1722no—
197C22⋊C8—22no—
198#97—41no—
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—
208#95—861no—
209C2×Q8—21no—
210C2×Q8—21no—
211C2×Q8—41no—
212C2×Q8—41no—
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—1722no—
225M16—1722no—
226C2×C8—42no—
227C2×C8—1722no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—1721no—
232C4⋊C4—1721no—
233C4⋊C4—1722no—
234C4⋊C4—1722no—
235C4⋊C4—1721no—
236C4⋊C4—1721no—
237C4⋊C4—1721no—
238C4⋊C4—1721no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C23C2×(C2×D43)⋊C411yescharacteristic
246Q8—42no—
247Q8—42no—
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—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
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—1721no—
274C2×C4#1306323911yescharacteristic
275C2×C4#1306323911yescharacteristic
276C2×C4#1306335311yescharacteristic
277C2×C4#1306335811yescharacteristic
278C8—82no—
279C8—3442no—
280C22—21no—
281C22—21no—
282C22C2×#1306323911yescharacteristic
283C22#1458290111yescharacteristic
284C22#1458291511yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—3441no—
295C4—3441no—
296C4—3441no—
297C4—3441no—
298C2—21no—
299C2—21no—
300C2#1913313911yescharacteristic
301C2#1913624811yescharacteristic
302C2#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#11835
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
174. C43#11835semidirect

Maximal subgroups

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

subgroupindex
#191404712
#191345912
#191326232
#191326022
C43×#14672
#1183543