Finite Group Databasebeta

← #25009546

Subgroups — #25009546

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#19135937C211yesmaximal, characteristic
3#19133569C211yesmaximal, characteristic
4#19132626C211yesmaximal, characteristic
5#19132601C211yesmaximal, characteristic
6#19132540C211yesmaximal, characteristic
7C43×#1611C211yesmaximal, characteristic
8#14583054—21no—
9#14582942—21no—
10#14582829—21no—
11#14582820—21no—
12#14582819C2211yescharacteristic
13#14582798—21no—
14#14582796—21no—
15#14582781—21no—
16#14582780—21no—
17#14582768C2211yescharacteristic
18#14582668C2211yescharacteristic
19#14582658—21no—
20#14582636—21no—
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#483—21no—
24C43×#398C2211yescharacteristic
25C43×#328—21no—
26C43×#324C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×#10621885—41no—
29C2×#10621877—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43D411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43D411yescharacteristic
39#13063258—41no—
40#13063256—41no—
41#13063248—41no—
42C22⋊(C43⋊C8)—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95D411yescharacteristic
49C4⋊Q8×C43—41no—
50#125×C43—41no—
51C22⋊Q8×C43—21no—
52C22⋊Q8×C43—21no—
53#117×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C4⋊C4×C43C2311yescharacteristic
57#106×C43—41no—
58#103×C43—41no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62C2×Q8×C43—21no—
63C2×Q8×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C2×Dic86—41no—
74C2×Dic86—81no—
75C2×C8×C43—41no—
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C42×C43—41no—
88#10621885—82no—
89C4⋊Dic43—41no—
90C4⋊Dic43—81no—
91C4⋊Dic43—81no—
92Dic43⋊C4—24no—
93Dic43⋊C4—81no—
94Dic43⋊C4—81no—
95Dic43⋊C4—81no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—81no—
99#10621877—22no—
100#10621877—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C23×C43#12011yescharacteristic
104Q8×C43—81no—
105Q8×C43—81no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—22no—
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—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43#13511yescharacteristic
121C2×C4×C43#13711yescharacteristic
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—
133C2×Dic43—41no—
134Dic86—42no—
135Dic86—81no—
136C8×C43—81no—
137C43⋊C8—42no—
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—
151C4×C43—81no—
152C4×C43—81no—
153Dic43—42no—
154Dic43—42no—
155Dic43—81no—
156Dic43—81no—
157#2792—431no—
158#2060—431no—
159#1611D4311yescharacteristic
160#1605—431no—
161#1354—431no—
162#1346—431no—
163#1325—431no—
164C2×C43—21no—
165C2×C43—21no—
166C2×C43#160311yescharacteristic
167C2×C43#220011yescharacteristic
168C2×C43#220511yescharacteristic
169#544C2×D4311yescharacteristic
170#483—21no—
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#343—431no—
183#339—861no—
184#328—21no—
185#328—861no—
186#324—431no—
187#324C2×D4311yescharacteristic
188C43#1224011yescharacteristic, complemented, Sylow
189C22×Q8—431no—
190C2×Q16—1721no—
191C2×M16—861no—
192C4⋊Q8—41no—
193#125—41no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196#117—21no—
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⋊C4C22⋊D4311yescharacteristic
206C2×C4⋊C4C22×D4311yescharacteristic
207C2×C42—431no—
208C2×C42—861no—
209#107—1721no—
210#106—41no—
211#106—1721no—
212#103—41no—
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#95C22⋊D4311yescharacteristic
224C2×Q8—21no—
225C2×Q8—21no—
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×C4D4×D4311yescharacteristic
235C22×C4D4×D4311yescharacteristic
236C22×C4C2×C22⋊D4311yescharacteristic
237Q16—3442no—
238M16—862no—
239M16—1721no—
240C2×C8—41no—
241C2×C8—1721no—
242C2×C8—1721no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—864no—
254C4⋊C4—3441no—
255C4⋊C4—3441no—
256C4⋊C4—3441no—
257C4⋊C4—3441no—
258C4⋊C4—3441no—
259C4⋊C4—1721no—
260C22⋊C4—41no—
261C42—41no—
262C42—861no—
263C42—861no—
264C42—3441no—
265C23#1306329311yescharacteristic
266Q8—81no—
267Q8—81no—
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—41no—
283C2×C4—41no—
284C2×C4—862no—
285C2×C4—862no—
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#1306334611yescharacteristic
297C2×C4#1306335411yescharacteristic
298C8—81no—
299C8—3441no—
300C8—1722no—
301C22—21no—
302C22—21no—
303C22#1458305811yescharacteristic
304C22#1458308011yescharacteristic
305C22#1458308511yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—3441no—
315C4—3441no—
316C4—1722no—
317C4—1722no—
318C2—21no—
319C2—21no—
320C2#1913355511yescharacteristic
321C2#1913659911yescharacteristic
322C2#1913662411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1611C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1611D43
hypocenterC43#12240
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1611

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
#191359372
#191335692
#191326262
#191326012
#191325402
C43×#16112
#1224043