Finite Group Databasebeta

← #25009682

Subgroups — #25009682

Order 11008.

330 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 57 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#19142868C211yesmaximal, characteristic
2#19135946C211yesmaximal, characteristic
3#19133639C211yesmaximal, characteristic
4#19133636C211yesmaximal, characteristic
5#19132621C211yesmaximal, characteristic
6#19132538C211yesmaximal, characteristic
7C43×#1353C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9#14583235—21no—
10#14583234—21no—
11#14582941—21no—
12#14582840—21no—
13#14582839—21no—
14#14582838C2211yescharacteristic
15#14582820—21no—
16#14582820—21no—
17#14582819—21no—
18#14582764C2211yescharacteristic
19#14582763—21no—
20#14582660—21no—
21#14582637—21no—
22#14582635—21no—
23#14582625C2211yescharacteristic
24C43×#400C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86—21no—
28#13063324—41no—
29#13063316—41no—
30#13063304—21no—
31#13063304—21no—
32#13063284—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×C4×Dic43D411yescharacteristic
40#13063259—41no—
41#13063259—41no—
42#13063258—41no—
43#13063257—41no—
44#13063250—41no—
45#13063248—41no—
46C22⋊(C43⋊C8)—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95D411yescharacteristic
55C2×M16×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C4⋊C4×C43C2311yescharacteristic
58C22⋊C8×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×Dic86—21no—
72C2×Dic86—21no—
73C2×Dic86—81no—
74C2×Dic86—81no—
75C2×Dic86—81no—
76M16×C43—22no—
77M16×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C22⋊Dic43—41no—
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89C4⋊Dic43—81no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92Dic43⋊C4—81no—
93Dic43⋊C4—81no—
94Dic43⋊C4—81no—
95C4×Dic43—21no—
96C4×Dic43—41no—
97C4×Dic43Q1612yes—
98C2×C43⋊C8—41no—
99C23×C43#12011yescharacteristic
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43C2×Q1611yescharacteristic
113C2×C4×C43#13711yescharacteristic
114C2×Dic43—22no—
115C2×Dic43—41no—
116C2×Dic43—41no—
117C2×Dic43—41no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128Dic86—84no—
129Dic86—81no—
130Dic86—81no—
131C8×C43—42no—
132C8×C43—81no—
133C43⋊C8—81no—
134#12261—431nomaximal, Sylow
135C22×C43—21no—
136C22×C43—21no—
137C22×C43#45111yescharacteristic
138C22×C43#45611yescharacteristic
139C22×C43B(4,𝔽2)11yescharacteristic
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—41no—
143C4×C43—41no—
144C4×C43—81no—
145C4×C43—81no—
146Dic43—42no—
147Dic43—81no—
148Dic43—81no—
149Dic43—81no—
150Dic43—81no—
151Dic43—81no—
152#2844—431no—
153#2061—431no—
154#1617—431no—
155#1617—431no—
156#1353—431no—
157#1353D4311yescharacteristic
158#1324—431no—
159C2×C43—21no—
160C2×C43—21no—
161C2×C43#160511yescharacteristic
162C2×C43#220111yescharacteristic
163C2×C43#220211yescharacteristic
164#544—431no—
165#484—861no—
166#484—861no—
167#428—861no—
168#400—431no—
169#400—861no—
170#400—861no—
171#400C2×D4311yescharacteristic
172#395—861no—
173#395—861no—
174#395—861no—
175#382—431no—
176#382—861no—
177#343C2×D4311yescharacteristic
178#339—861no—
179#328—861no—
180#328—861no—
181#324—431no—
182#324C2×D4311yescharacteristic
183C43#1226111yescharacteristic, complemented, Sylow
184C22×Q8—861no—
185C2×M16—21no—
186C4⋊Q8—1721no—
187#125—1721no—
188C22⋊Q8—861no—
189C22⋊Q8—861no—
190#117—861no—
191C2×C4⋊C4—431no—
192C2×C4⋊C4—431no—
193C2×C4⋊C4—861no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4D17211yescharacteristic
198C2×C4⋊C4C22×D4311yescharacteristic
199C2×C42—431no—
200#107—1721no—
201#107—1721no—
202#107—1721no—
203#106—1721no—
204#103—1721no—
205#103—1721no—
206C22⋊C8—21no—
207C22⋊C8—861no—
208#95—21no—
209#95—21no—
210#95—431no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—861no—
218#95D17211yescharacteristic
219C2×Q8—861no—
220C2×Q8—861no—
221C2×Q8—3441no—
222C2×Q8—3441no—
223C2×Q8—3441no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—861no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4C2×D17211yescharacteristic
231C22×C4D4×D4311yescharacteristic
232C22×C4D4×D4311yescharacteristic
233M16—22no—
234M16—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—1721no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—861no—
241C4⋊C4—861no—
242C4⋊C4—861no—
243C4⋊C4—861no—
244C4⋊C4—3441no—
245C4⋊C4—3441no—
246C4⋊C4—3441no—
247C4⋊C4—3441no—
248C4⋊C4—1721no—
249C4⋊C4—1721no—
250C4⋊C4—1721no—
251C4⋊C4—1721no—
252C22⋊C4—1721no—
253C42—432no—
254C42—861no—
255C42—1721no—
256C23#1306329511yescharacteristic
257Q8—3441no—
258Q8—3441no—
259Q8—3444no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—862no—
273C2×C4—1721no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4Q16×D4311yescharacteristic
287C2×C4#1306335411yescharacteristic
288C8—42no—
289C8—81no—
290C8—3441no—
291C22—21no—
292C22—21no—
293C22#1458305611yescharacteristic
294C22#1458308311yescharacteristic
295C22#1458308711yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—81no—
301C4—81no—
302C4—3441no—
303C4—3441no—
304C4—3441no—
305C4—3441no—
306C4—3441no—
307C4—1722no—
308C2—21no—
309C2—21no—
310C2#1913357011yescharacteristic
311C2#1913660911yescharacteristic
312C2#1913661311yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1353C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1353D43
hypocenterC43#12261
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
183. C43#12261semidirect

Maximal subgroups

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

subgroupindex
#191428682
#191359462
#191336392
#191336362
#191326212
#191325382
C43×#13532
#1226143