Finite Group Databasebeta

← #25009783

Subgroups — #25009783

Order 11008.

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

normal subgroups only

This group has 362 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#19142738C211yesmaximal, characteristic
2#19133603C211yesmaximal, characteristic, complemented
3#19133569C211yesmaximal, characteristic, complemented
4#19132624C211yesmaximal, characteristic, complemented
5#19132600C211yesmaximal, characteristic, complemented
6#19132527C211yesmaximal, characteristic
7C43×#2027C211yesmaximal, characteristic
8#14583227—21no—
9#14583054—21no—
10#14582829C2211yescharacteristic
11#14582827—21no—
12#14582827—21no—
13#14582822—21no—
14#14582819C2211yescharacteristic
15#14582813—21no—
16#14582811—21no—
17#14582783—21no—
18#14582636—21no—
19#14582636—21no—
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#418—21no—
24C43×#390C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#339—21no—
27C22×Dic86D411yescharacteristic
28C2×#10621885—41no—
29C2×C4⋊Dic43D411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37#13063256—41no—
38#13063249—41no—
39#13063248—41no—
40C22⋊(C43⋊C8)—21no—
41C22⋊(C43⋊C8)—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95D411yescharacteristic
48C43⋊#95D411yescharacteristic
49C22×D4×C43D411yescharacteristic
50C2×M16×C43—21no—
51C4⋊Q8×C43—41no—
52#125×C43—41no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55#117×C43—21no—
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C42×C43D411yescharacteristic
60#102×C43—41no—
61#102×C43—41no—
62C24×C43—21no—
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C22×C4×C43—21no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×Dic86—41no—
78C2×Dic86—81no—
79M16×C43—41no—
80M16×C43—41no—
81C2×C8×C43—41no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43—81no—
91C22⋊C4×C43—81no—
92C42×C43—41no—
93C42×C43—41no—
94C22⋊Dic43—81no—
95C22⋊Dic43—81no—
96C22⋊Dic43—81no—
97C22⋊Dic43—81no—
98#10621885—82no—
99C4⋊Dic43—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102Dic43⋊C4—81no—
103Dic43⋊C4—81no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43#12011yescharacteristic
114Q8×C43—81no—
115Q8×C43—81no—
116D4×C43—42no—
117D4×C43—81no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43#13511yescharacteristic
130C2×C4×C43#13711yescharacteristic
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143Dic86—42no—
144Dic86—81no—
145C8×C43—81no—
146C43⋊C8—81no—
147C43⋊C8—81no—
148#12276—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—81no—
152C22×C43—81no—
153C22×C43—81no—
154C22×C43—81no—
155C22×C43—81no—
156C22×C43—81no—
157C22×C43—81no—
158C22×C43#45211yescharacteristic
159C22×C43#45511yescharacteristic
160C22×C43B(4,𝔽2)11yescharacteristic
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—81no—
166C4×C43—81no—
167C4×C43—81no—
168Dic43—81no—
169Dic43—81no—
170Dic43—81no—
171Dic43—81no—
172#2830—431no—
173#2027D4311yescharacteristic
174#1611—431no—
175#1605—431no—
176#1354—431no—
177#1346—431no—
178#1318—431no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—161no—
182C2×C43#160611yescharacteristic
183C2×C43#220011yescharacteristic
184C2×C43#220311yescharacteristic
185#544C2×D4311yescharacteristic
186#483—861no—
187#451—861no—
188#418—21no—
189#398—431no—
190#397—861no—
191#397—861no—
192#396—861no—
193#395—431no—
194#394—861no—
195#393—861no—
196#390C2×D4311yescharacteristic
197#387—861no—
198#343C2×D4311yescharacteristic
199#339—21no—
200#328—861no—
201#328—861no—
202#324—431no—
203#324—431no—
204C43#1227611yescharacteristic, complemented, Sylow
205C22×Q8—431no—
206C22×D4C22⋊D4311yescharacteristic
207C2×Q16—1721no—
208C2×M16—21no—
209C4⋊Q8—41no—
210#125—41no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213#117—21no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4C22×D4311yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223C2×C22⋊C4—861no—
224C2×C22⋊C4—861no—
225C2×C42C22⋊D4311yescharacteristic
226#106—1721no—
227#103—1721no—
228#103—1721no—
229#102—41no—
230#102—41no—
231C22⋊C8—861no—
232C22⋊C8—861no—
233#95—431no—
234#95—431no—
235#95—861no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95—861no—
240C24—21no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—3441no—
244C2×Q8—1721no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4D4×D4311yescharacteristic
255C22×C4D4×D4311yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257Q16—3442no—
258M16—41no—
259M16—41no—
260C2×C8—41no—
261C2×C8—1721no—
262C2×C8—1721no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—3441no—
271C4⋊C4—3441no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C22⋊C4—41no—
276C22⋊C4—81no—
277C22⋊C4—81no—
278C22⋊C4—3441no—
279C22⋊C4—3441no—
280C22⋊C4—3441no—
281C22⋊C4—3441no—
282C42—41no—
283C42—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23#1306329311yescharacteristic
292Q8—81no—
293Q8—81no—
294Q8—3441no—
295Q8—1722no—
296D4—42no—
297D4—81no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4#1306334511yescharacteristic
322C2×C4#1306335611yescharacteristic
323C8—81no—
324C8—3441no—
325C8—3441no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1458305911yescharacteristic
336C22#1458307611yescharacteristic
337C22#1458308511yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—3441no—
346C4—3441no—
347C4—3441no—
348C4—3441no—
349C2—21no—
350C2—21no—
351C2—161no—
352C2#1913357311yescharacteristic
353C2#1913660111yescharacteristic
354C2#1913661511yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2027C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
hypercenter#2027D43
hypocenterC43#12276
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2027

Complements

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

NH ≅ G/Ntype
2. #19133603C2semidirect
3. #19133569C2semidirect
4. #19132624C2semidirect
5. #19132600C2semidirect
204. C43#12276semidirect

Maximal subgroups

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

subgroupindex
#191427382
#191336032
#191335692
#191326242
#191326002
#191325272
C43×#20272
#1227643