Finite Group Databasebeta

← #25015287

Subgroups — #25015287

Order 11008.

396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 99 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#19139782C211yesmaximal, characteristic
2C4×#13063244C211yesmaximal, characteristic
3#19132721C212yesmaximal
4#19132721C212yesmaximal
5C43×#1801C211yesmaximal, characteristic
6C2×#13063317C411yescharacteristic
7C2×#13063244C2212yes—
8C4×#10621877—21no—
9#14582832—21no—
10#14582832—21no—
11#14582806C2211yescharacteristic
12#14582806C2211yescharacteristic
13#14582783—21no—
14#14582783—21no—
15#14582768C411yescharacteristic
16#14582764C411yescharacteristic
17C4×C4⋊Dic43C411yescharacteristic
18#14582668—21no—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#423—21no—
21C2×#101×C43C2212yes—
22C43×#343—21no—
23C2×#10621877—22no—
24#13063317—41no—
25#13063317—41no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43C2×C411yescharacteristic
35#13063244—22no—
36#13063244Q814yes—
37#13063236—41no—
38C4×C43⋊C8—41no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C22×Q8×C43C2311yescharacteristic
47C2×M16×C43—22no—
48C4×Q8×C43—41no—
49C4×Q8×C43—41no—
50C2×C4⋊C4×C43C2×C411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C42×C43C2×C411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C2×C42×C43D411yescharacteristic
56C4⋊C8×C43—41no—
57C4⋊C8×C43—41no—
58#101×C43—24no—
59C2×Q8×C43—41no—
60C2×Q8×C43—41no—
61C2×Q8×C43C2×Q812yes—
62C2×Q8×C43#4112yes—
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74M16×C43—42no—
75M16×C43—42no—
76C2×C8×C43—42no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C42×C43—21no—
81C42×C43—21no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C4⋊Dic43—42no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89Dic43⋊C4—42no—
90Dic43⋊C4—42no—
91Dic43⋊C4—42no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94C4×Dic43—41no—
95C4×Dic43—41no—
96#10621877—24no—
97#10621877—42no—
98C2×C43⋊C8—42no—
99C23×C43C2×C22⋊C411yescharacteristic
100Q8×C43—42no—
101Q8×C43—42no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43#9911yescharacteristic
116C2×C4×C43#9911yescharacteristic
117C2×C4×C43C4×Q812yes—
118C2×C4×C43C22⋊Q812yes—
119C2×C4×C43#12411yescharacteristic
120C2×C4×C43C4⋊Q811yescharacteristic
121C2×Dic43—22no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—42no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C8×C43—82no—
133C43⋊C8—44no—
134#13303—431nomaximal, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43#39111yescharacteristic
138C22×C43C2×#9911yescharacteristic
139C22×C43#41011yescharacteristic
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—22no—
143C4×C43—21no—
144C4×C43—22no—
145C4×C43—21no—
146C4×C43—41no—
147C4×C43—41no—
148C4×C43—41no—
149Dic43—42no—
150Dic43—81no—
151Dic43—81no—
152Dic43—81no—
153#2565—431no—
154#1801D4311yescharacteristic
155C4×#101—431no—
156#1394—432no—
157#1394—432no—
158C2×C43—21no—
159C2×C43—21no—
160C2×C43#199611yescharacteristic
161C2×C43#213211yescharacteristic
162C2×C43#213311yescharacteristic
163C2×#125—431no—
164C2×C4×Q8C2×D4311yescharacteristic
165#423—21no—
166C2×#101—432no—
167C2×#101C2×D4312yes—
168C4×M16—861no—
169#398—861no—
170#398—861no—
171#391—431no—
172#391—431no—
173#387—861no—
174#387—861no—
175#384—431no—
176#382—431no—
177C4×C4⋊C4—431no—
178#343—21no—
179#343—861no—
180C43#1330311yescharacteristic, complemented, Sylow
181C22×Q8C22×D4311yescharacteristic
182C2×M16—22no—
183C2×M16—862no—
184#125—1721no—
185#125—1721no—
186C4×Q8—41no—
187C4×Q8—41no—
188C2×C4⋊C4—431no—
189C2×C4⋊C4—431no—
190C2×C4⋊C4—861no—
191C2×C4⋊C4—861no—
192C2×C4⋊C4—861no—
193C2×C4⋊C4—861no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4C4×D4311yescharacteristic
196C2×C4⋊C4D17211yescharacteristic
197C2×C4⋊C4C22⋊D4311yescharacteristic
198C2×C42—431no—
199C2×C42—431no—
200C2×C42C4×D4311yescharacteristic
201C2×C42D17211yescharacteristic
202C2×C42C22⋊D4311yescharacteristic
203C4⋊C8—41no—
204C4⋊C8—41no—
205#101—24no—
206#101—434no—
207#101—862no—
208#97—1721no—
209C4×C8—1721no—
210#95—861no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8#1062190012yes—
220C2×Q8Q8×D4312yes—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4—861no—
225C22×C4(C2×D43)⋊C411yescharacteristic
226C22×C4(C2×D43)⋊C411yescharacteristic
227C22×C4(C2×D43)⋊C411yescharacteristic
228C22×C4(C2×D43)⋊C411yescharacteristic
229C22×C4C2×C4×D4311yescharacteristic
230C22×C4C2×D17211yescharacteristic
231C22×C4C2×C22⋊D4311yescharacteristic
232M16—42no—
233M16—42no—
234M16—864no—
235M16—1722no—
236C2×C8—42no—
237C2×C8—1722no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—1721no—
242C4⋊C4—1721no—
243C4⋊C4—1722no—
244C4⋊C4—1722no—
245C4⋊C4—1722no—
246C4⋊C4—1722no—
247C4⋊C4—1721no—
248C4⋊C4—1721no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—1721no—
256C42—1721no—
257C23C2×(C2×D43)⋊C411yescharacteristic
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—862no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1722no—
279C2×C4—1721no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4#1306323911yescharacteristic
285C2×C4#1306323911yescharacteristic
286C2×C4#1306329012yes—
287C2×C4#1306330512yes—
288C2×C4#1306331211yescharacteristic
289C2×C4#1306332311yescharacteristic
290C8—82no—
291C8—1724no—
292C22—21no—
293C22—21no—
294C22#1458280411yescharacteristic
295C22C2×#1306323911yescharacteristic
296C22#1458287211yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—22no—
301C4—22no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—3441no—
307C4—3441no—
308C4—3441no—
309C4—1722no—
310C2—21no—
311C2—21no—
312C2#1913557911yescharacteristic
313C2#1913627811yescharacteristic
314C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#1801C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC22×Q8×C43C23
hypercenter#1801D43
hypocenterC43#13303
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
180. C43#13303semidirect

Maximal subgroups

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

subgroupindex
#191397822
C4×#130632442
#191327212
C43×#18012
#1330343