Finite Group Databasebeta

← #24991669

Subgroups — #24991669

Order 11008.

484 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 103 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#19143680C211yesmaximal, characteristic
2#19137886C211yesmaximal, characteristic
3#19133043C212yesmaximal
4#19132489C212yesmaximal
5C4×#101×C43C211yesmaximal, characteristic
6C2×C4×Dic86C2211yescharacteristic
7#14583030—24no—
8#14582956—21no—
9#14582956C2212yes—
10#14582952—21no—
11#14582830—21no—
12#14582829C411yescharacteristic
13#14582829C411yescharacteristic
14#14582819C411yescharacteristic
15#14582819C411yescharacteristic
16#14582818—21no—
17C4×Dic43⋊C4—21no—
18C4×Dic43⋊C4—21no—
19#14582745C2211yescharacteristic
20#14582631—24no—
21C2×C4×Q8×C43C2211yescharacteristic
22C2×#101×C43—21no—
23C4×M16×C43C2212yes—
24C43×#343—21no—
25C22×Dic86C2×C411yescharacteristic
26C4×Dic86—22no—
27C4×Dic86—22no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×C4×Dic43—21no—
35C2×C4×Dic43—21no—
36C4⋊(C43⋊C8)—22no—
37C4⋊(C43⋊C8)—22no—
38C4⋊(C43⋊C8)D414yes—
39C22⋊(C43⋊C8)—22no—
40#13063236—22no—
41#13063236—22no—
42C4×C43⋊C8—22no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95C2×C411yescharacteristic
49C43⋊#95C2×C411yescharacteristic
50C22×Q8×C43D411yescharacteristic
51C2×M16×C43—22no—
52C4×Q8×C43—22no—
53C4×Q8×C43—22no—
54C2×C4⋊C4×C43C2×C411yescharacteristic
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60#101×C43—24no—
61#97×C43—22no—
62C4×C8×C43—22no—
63C2×Q8×C43—22no—
64C2×Q8×C43—22no—
65C2×Q8×C43—41no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×Dic86—22no—
78C2×Dic86—42no—
79M16×C43—24no—
80M16×C43—42no—
81C2×C8×C43—42no—
82C4⋊C4×C43—22no—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—22no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—21no—
89C42×C43C2×D412yes—
90C42×C43#4112yes—
91C4⋊Dic43—22no—
92Dic43⋊C4—42no—
93Dic43⋊C4—42no—
94Dic43⋊C4—42no—
95Dic43⋊C4—42no—
96Dic43⋊C4—42no—
97C4×Dic43—24no—
98C4×Dic43—41no—
99C4×Dic43—41no—
100C2×C43⋊C8—24no—
101C23×C43C2×C22⋊C411yescharacteristic
102Q8×C43—44no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43#10412yes—
117C2×C4×C43C4×D412yes—
118C2×C4×C43#12011yescharacteristic
119C2×C4×C43#12112yes—
120C2×C4×C43#12311yescharacteristic
121C2×Dic43—22no—
122C2×Dic43—22no—
123C2×Dic43—22no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133Dic86—24no—
134Dic86—42no—
135C8×C43—44no—
136C43⋊C8—44no—
137#9030—431nomaximal, Sylow
138C22×C43—21no—
139C22×C43—21no—
140C22×C43#38611yescharacteristic
141C22×C43C2×#10411yescharacteristic
142C22×C43#42111yescharacteristic
143C4×C43—22no—
144C4×C43—22no—
145C4×C43—21no—
146C4×C43—22no—
147C4×C43—41no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43#45612yes—
151Dic43—42no—
152Dic43—42no—
153Dic43—42no—
154Dic43—81no—
155#2983—431no—
156#2399—431no—
157C4×#101D4311yescharacteristic
158#1491—432no—
159#1300—432no—
160C2×C43—21no—
161C2×C43—21no—
162C2×C43#187111yescharacteristic
163C2×C43#188611yescharacteristic
164C2×C43#189111yescharacteristic
165C2×C4×Q8—431no—
166C2×C4×Q8C2×D4311yescharacteristic
167#446—864no—
168#432—432no—
169#432—861no—
170#431—861no—
171C2×#101—21no—
172C4×M16C2×D4312yes—
173#398—431no—
174#398—431no—
175#398—861no—
176#395—431no—
177#395—431no—
178#395—861no—
179C4×C4⋊C4—861no—
180C4×C4⋊C4—861no—
181#376—431no—
182#343—21no—
183Q8⋊C8—864no—
184C43#903011yescharacteristic, complemented, Sylow
185C22×Q8—431no—
186C22×Q8C22⋊D4311yescharacteristic
187C2×M16—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—862no—
191C4×Q8—862no—
192C2×C4⋊C4—431no—
193C2×C4⋊C4—861no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4—861no—
198C2×C4⋊C4C4×D4311yescharacteristic
199C2×C4⋊C4C4×D4311yescharacteristic
200C2×C4⋊C4C22⋊D4311yescharacteristic
201C2×C42—861no—
202C2×C42—861no—
203C2×C42D17211yescharacteristic
204C2×C42D17211yescharacteristic
205C2×C42C22×D4311yescharacteristic
206C4⋊C8—434no—
207C4⋊C8—862no—
208C4⋊C8—862no—
209#101—24no—
210C22⋊C8—862no—
211#97—22no—
212#97—862no—
213#97—862no—
214C4×C8—22no—
215C4×C8—862no—
216#95—431no—
217#95—431no—
218#95—861no—
219#95—861no—
220#95—861no—
221#95—861no—
222#95—861no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—862no—
227C2×Q8—1722no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4—861no—
232C22×C4(C2×D43)⋊C411yescharacteristic
233C22×C4(C2×D43)⋊C411yescharacteristic
234C22×C4(C2×D43)⋊C411yescharacteristic
235C22×C4(C2×D43)⋊C411yescharacteristic
236C22×C4C2×C4×D4311yescharacteristic
237C22×C4C2×D17211yescharacteristic
238C22×C4C2×C22⋊D4311yescharacteristic
239M16—24no—
240M16—42no—
241C2×C8—42no—
242C2×C8—864no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—862no—
247C4⋊C4—1722no—
248C4⋊C4—1722no—
249C4⋊C4—1722no—
250C4⋊C4—1722no—
251C4⋊C4—1722no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—864no—
257C42—1721no—
258C42—1721no—
259C42D4×D4312yes—
260C42#1062190012yes—
261C23C2×(C2×D43)⋊C411yescharacteristic
262Q8—44no—
263Q8—864no—
264Q8—1722no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—862no—
279C2×C4—862no—
280C2×C4—862no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4#1306325312yes—
291C2×C4(C22⋊D43)⋊C412yes—
292C2×C4#1306329511yescharacteristic
293C2×C4#1306329712yes—
294C2×C4#1306330911yescharacteristic
295C8—44no—
296C8—1724no—
297C22—21no—
298C22—21no—
299C22#1458277611yescharacteristic
300C22C2×#1306325311yescharacteristic
301C22#1458291711yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—3441no—
310C4—1722no—
311C4—1722no—
312C4—1722no—
313C4#1458308412yes—
314C2—21no—
315C2—21no—
316C2#1913489511yescharacteristic
317C2#1913498611yescharacteristic
318C2#1913501111yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#101×C43C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenterC4×#101D43
hypocenterC43#9030
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
184. C43#9030semidirect

Maximal subgroups

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

subgroupindex
#191436802
#191378862
#191330432
#191324892
C4×#101×C432
#903043