Finite Group Databasebeta

← #24985736

Subgroups — #24985736

Order 11008.

338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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#19142586C211yesmaximal, characteristic
2#19136154C211yesmaximal, characteristic
3#19136073C211yesmaximal, characteristic
4#19136066C211yesmaximal, characteristic
5#19132419C211yesmaximal, characteristic
6#19132417C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic
8C2×#13063258—21no—
9C2×#13063257—21no—
10#14582839—21no—
11#14582838—21no—
12#14582837—21no—
13#14582797C2211yescharacteristic
14#14582797C2211yescharacteristic
15#14582786—21no—
16#14582785—21no—
17#14582780—21no—
18#14582769C2211yescharacteristic
19#14582662—21no—
20#14582662—21no—
21#14582662—21no—
22#14582661—21no—
23#14582654C2211yescharacteristic
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C43⋊C8—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4⋊Dic43D411yescharacteristic
33C2×C4⋊Dic43D411yescharacteristic
34C2×C4⋊Dic43D411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×C4×Dic43—21no—
38#13063258—42no—
39#13063257—42no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C22×C8×C43—21no—
50C22×C8×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C42×C43C2311yescharacteristic
55#95×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—21no—
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43—21no—
65C22×Dic43—41no—
66C2×C8×C43—22no—
67C2×C8×C43—41no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C42×C43—41no—
78C4⋊Dic43—21no—
79C4⋊Dic43—21no—
80C4⋊Dic43—21no—
81C4⋊Dic43—21no—
82C4⋊Dic43—41no—
83C4⋊Dic43—41no—
84C4⋊Dic43—42no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89Dic43⋊C4—41no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92Dic43⋊C4—41no—
93C4×Dic43—81no—
94C2×C43⋊C8—22no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8—41no—
97C23×C43#12011yescharacteristic
98C2×C4×C43—21no—
99C2×C4×C43—21no—
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#13511yescharacteristic
111C2×C4×C43#13511yescharacteristic
112C2×C4×C43#13511yescharacteristic
113C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C43#13711yescharacteristic
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—
128C2×Dic43—81no—
129C2×Dic43—81no—
130C2×Dic43—81no—
131C8×C43—42no—
132C8×C43—81no—
133C43⋊C8—42no—
134#7803—431nomaximal, Sylow
135C22×C43#44911yescharacteristic
136C22×C43#44911yescharacteristic
137C22×C43#45211yescharacteristic
138C22×C43#45411yescharacteristic
139C22×C43#45611yescharacteristic
140C22×C43#45611yescharacteristic
141C22×C43#45811yescharacteristic
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—81no—
149C4×C43—81no—
150Dic43—81no—
151Dic43—81no—
152Dic43—81no—
153Dic43—81no—
154Dic43—161no—
155#2810—431no—
156#2099—431no—
157#2084—431no—
158#2083—431no—
159#1271—431no—
160#1271—431no—
161#1271D4311yescharacteristic
162C2×C43#160911yescharacteristic
163C2×C43#160911yescharacteristic
164C2×C43#161511yescharacteristic
165C2×C43#162811yescharacteristic
166C2×C43#165011yescharacteristic
167C2×C43#165211yescharacteristic
168C2×C43#166311yescharacteristic
169C2×#107—861no—
170C2×#106—861no—
171#400—861no—
172#400—861no—
173#400—861no—
174#389—431no—
175#389—431no—
176#389C2×D4311yescharacteristic
177#387—861no—
178#387—861no—
179#387—861no—
180#384—431no—
181#340—861no—
182#340—861no—
183#340—861no—
184#340—861no—
185#336—431no—
186#336C2×D4311yescharacteristic
187#336C2×D4311yescharacteristic
188C43#780311yescharacteristic, complemented, Sylow
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—861no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—431no—
194C2×C4⋊C4—431no—
195C2×C4⋊C4—431no—
196C2×C4⋊C4—431no—
197C2×C4⋊C4—861no—
198C2×C4⋊C4—861no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4—861no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4D17211yescharacteristic
203C2×C4⋊C4D17211yescharacteristic
204C2×C42—861no—
205C2×C42C22×D4311yescharacteristic
206#107—1722no—
207#106—1722no—
208#95—21no—
209#95—861no—
210#95—861no—
211#95—861no—
212#95—861no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—861no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4—1721no—
225C22×C4C2×D17211yescharacteristic
226C22×C4D4×D4311yescharacteristic
227C22×C4D4×D4311yescharacteristic
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—862no—
235C2×C8—1721no—
236C2×C8—1721no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—861no—
243C4⋊C4—861no—
244C4⋊C4—861no—
245C4⋊C4—861no—
246C4⋊C4—1722no—
247C4⋊C4—1721no—
248C4⋊C4—1721no—
249C4⋊C4—1721no—
250C4⋊C4—1721no—
251C4⋊C4—1721no—
252C4⋊C4—1721no—
253C4⋊C4—1721no—
254C4⋊C4—1721no—
255C4⋊C4—1721no—
256C4⋊C4—1721no—
257C42—41no—
258C42—3441no—
259C23#1306329511yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—3441no—
273C2×C4—3441no—
274C2×C4—3441no—
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×C4—1721no—
287C2×C4#1306334611yescharacteristic
288C2×C4#1306334611yescharacteristic
289C2×C4#1306334711yescharacteristic
290C2×C4#1306334911yescharacteristic
291C2×C4#1306335311yescharacteristic
292C2×C4#1306335711yescharacteristic
293C8—42no—
294C8—81no—
295C8—1722no—
296C22#1458304511yescharacteristic
297C22#1458304611yescharacteristic
298C22#1458306411yescharacteristic
299C22#1458307311yescharacteristic
300C22#1458308311yescharacteristic
301C22#1458308411yescharacteristic
302C22#1458309011yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—3441no—
312C4—3441no—
313C4—3441no—
314C4—3441no—
315C4—6881no—
316C2#1913359311yescharacteristic
317C2#1913359411yescharacteristic
318C2#1913362911yescharacteristic
319C2#1913370711yescharacteristic
320C2#1913385211yescharacteristic
321C2#1913386711yescharacteristic
322C2#1913392511yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socle, prime radicalC23×C43#120
hypercenter#1271D43
hypocenterC43#7803
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
188. C43#7803semidirect

Maximal subgroups

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

subgroupindex
#191425862
#191361542
#191360732
#191360662
#191324192
#191324172
C43×#12712
#780343