Finite Group Databasebeta

← #25009550

Subgroups — #25009550

Order 11008.

350 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 55 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#19142395C211yesmaximal, characteristic
2#19135941C211yesmaximal, characteristic
3#19133602C211yesmaximal, characteristic
4#19133571C211yesmaximal, characteristic
5#19132624C211yesmaximal, characteristic
6#19132540C211yesmaximal, characteristic
7C43×#1346C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9#14583229—21no—
10#14583057—21no—
11#14582941—21no—
12#14582829—21no—
13#14582820—21no—
14#14582819C2211yescharacteristic
15#14582798—21no—
16#14582796—21no—
17#14582781—21no—
18#14582780—21no—
19#14582768C2211yescharacteristic
20#14582660—21no—
21#14582637—21no—
22#14582635—21no—
23#14582625C2211yescharacteristic
24C43×#398C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×Dic172—41no—
29#13063324—41no—
30#13063316—41no—
31#13063304—21no—
32#13063304—21no—
33#13063284—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×C4×Dic43—21no—
42C2×C4×Dic43D411yescharacteristic
43#13063259—41no—
44#13063257—41no—
45#13063256—41no—
46#13063250—41no—
47#13063248—41no—
48C22⋊(C43⋊C8)—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×C43—21no—
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C4⋊C4×C43C2311yescharacteristic
59C22⋊C8×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—41no—
74C2×Dic86—81no—
75M16×C43—22no—
76M16×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C22⋊Dic43—41no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—41no—
89C4⋊Dic43—81no—
90C4⋊Dic43—81no—
91Dic43⋊C4—24no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—81no—
95Dic43⋊C4—81no—
96Dic43⋊C4—81no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—41no—
100C4×Dic43—81no—
101C2×C43⋊C8—41no—
102Dic172—82no—
103C23×C43#12011yescharacteristic
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43#13511yescharacteristic
117C2×C4×C43#13711yescharacteristic
118C2×Dic43—22no—
119C2×Dic43—22no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132Dic86—42no—
133Dic86—81no—
134Dic86—81no—
135Dic86—81no—
136C8×C43—42no—
137C8×C43—81no—
138C43⋊C8—81no—
139#12240—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43#45211yescharacteristic
143C22×C43#45611yescharacteristic
144C22×C43B(4,𝔽2)11yescharacteristic
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—42no—
148C4×C43—41no—
149C4×C43—41no—
150C4×C43—81no—
151Dic43—42no—
152Dic43—42no—
153Dic43—81no—
154Dic43—81no—
155Dic43—81no—
156Dic43—81no—
157#2792—431no—
158#2060—431no—
159#1611—431no—
160#1605—431no—
161#1354—431no—
162#1346D4311yescharacteristic
163#1325—431no—
164C2×C43—21no—
165C2×C43—21no—
166C2×C43#160311yescharacteristic
167C2×C43#220011yescharacteristic
168C2×C43#220511yescharacteristic
169#544—431no—
170#483—861no—
171#451—861no—
172#428—861no—
173#398—861no—
174#398C2×D4311yescharacteristic
175#395—431no—
176#395—861no—
177#389—861no—
178#389—861no—
179#387—861no—
180#387—861no—
181#384—431no—
182#343C2×D4311yescharacteristic
183#339—861no—
184#328—861no—
185#328—861no—
186#324—431no—
187#324C2×D4311yescharacteristic
188C43#1224011yescharacteristic, complemented, Sylow
189C22×Q8—431no—
190C2×Q16—1721no—
191C2×M16—21no—
192C4⋊Q8—1721no—
193#125—1721no—
194C22⋊Q8—861no—
195C22⋊Q8—861no—
196#117—861no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4—861no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4D17211yescharacteristic
206C2×C4⋊C4C22×D4311yescharacteristic
207C2×C42—431no—
208C2×C42—861no—
209#107—1721no—
210#106—1721no—
211#106—1721no—
212#103—1721no—
213#103—1721no—
214C22⋊C8—21no—
215C22⋊C8—861no—
216#95—21no—
217#95—431no—
218#95—861no—
219#95—861no—
220#95—861no—
221#95—861no—
222#95—861no—
223#95D17211yescharacteristic
224C2×Q8—861no—
225C2×Q8—861no—
226C2×Q8—3441no—
227C2×Q8—1721no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—861no—
231C22×C4—861no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4C2×D17211yescharacteristic
235C22×C4D4×D4311yescharacteristic
236C22×C4D4×D4311yescharacteristic
237Q16—3442no—
238M16—22no—
239M16—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—1721no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—864no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—3441no—
253C4⋊C4—3441no—
254C4⋊C4—3441no—
255C4⋊C4—3441no—
256C4⋊C4—3441no—
257C4⋊C4—1721no—
258C4⋊C4—1721no—
259C4⋊C4—1721no—
260C22⋊C4—1721no—
261C42—861no—
262C42—861no—
263C42—3441no—
264C42—1721no—
265C23#1306329511yescharacteristic
266Q8—3441no—
267Q8—3441no—
268Q8—3441no—
269Q8—1722no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—862no—
283C2×C4—862no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4#1306334411yescharacteristic
297C2×C4#1306335411yescharacteristic
298C8—42no—
299C8—81no—
300C8—3441no—
301C22—21no—
302C22—21no—
303C22#1458306211yescharacteristic
304C22#1458308311yescharacteristic
305C22#1458308711yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—3441no—
313C4—3441no—
314C4—3441no—
315C4—3441no—
316C4—1722no—
317C4—1722no—
318C2—21no—
319C2—21no—
320C2#1913355911yescharacteristic
321C2#1913660311yescharacteristic
322C2#1913662611yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1346C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1346D43
hypocenterC43#12240
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
188. C43#12240semidirect

Maximal subgroups

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

subgroupindex
#191423952
#191359412
#191336022
#191335712
#191326242
#191325402
C43×#13462
#1224043