Finite Group Databasebeta

← #25009785

Subgroups — #25009785

Order 11008.

362 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 59 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#19135751C211yesmaximal, characteristic
2#19133602C211yesmaximal, characteristic, complemented
3#19133568C211yesmaximal, characteristic, complemented
4#19132625C211yesmaximal, characteristic, complemented
5#19132601C211yesmaximal, characteristic, complemented
6#19132527C211yesmaximal, characteristic
7C43×#2830C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9#14583229—21no—
10#14583055—21no—
11#14582904—21no—
12#14582668C2211yescharacteristic
13#14582659—21no—
14#14582635—21no—
15#14582635—21no—
16#14582625C2211yescharacteristic
17#14582625C2211yescharacteristic
18C43×#398C2211yescharacteristic
19C43×#397—21no—
20C43×#397—21no—
21C43×#396—21no—
22C43×#395C2211yescharacteristic
23C43×#394—21no—
24C43×#393—21no—
25C43×#390C2211yescharacteristic
26C43×#387—21no—
27C2×#10621885—41no—
28C2×#10621877—21no—
29#13063324—41no—
30#13063316—41no—
31#13063304—21no—
32#13063304—21no—
33#13063284—21no—
34#13063256—41no—
35#13063249—41no—
36#13063248—41no—
37#13063246—41no—
38#13063246—41no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C22×Q8×C43D411yescharacteristic
42C22×D4×C43D411yescharacteristic
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43D411yescharacteristic
47C2×C4⋊C4×C43C2311yescharacteristic
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43—21no—
54C2×C42×C43D411yescharacteristic
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43D411yescharacteristic
61#95×C43D411yescharacteristic
62C24×C43—21no—
63C2×Q8×C43—41no—
64C2×Q8×C43—81no—
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C2×Dic86—21no—
78C2×Dic86—21no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—81no—
84C4⋊C4×C43—81no—
85C22⋊C4×C43—81no—
86C22⋊C4×C43—81no—
87C22⋊C4×C43—81no—
88C22⋊C4×C43—81no—
89C22⋊C4×C43—81no—
90C22⋊C4×C43—81no—
91C42×C43—41no—
92C22⋊Dic43—41no—
93#10621885—82no—
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100C4×Dic43—41no—
101#10621877—41no—
102#10621877—41no—
103C2×C43⋊C8—41no—
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—42no—
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—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×Dic43—41no—
142C2×Dic43—41no—
143Dic86—81no—
144Dic86—81no—
145C43⋊C8—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—
168C4×C43—81no—
169C4×C43—81no—
170Dic43—81no—
171Dic43—81no—
172#2830D4311yescharacteristic
173#2027—431no—
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#544—431no—
186#483—861no—
187#451—861no—
188#418—861no—
189#398C2×D4311yescharacteristic
190#397—21no—
191#397—21no—
192#396—21no—
193#395C2×D4311yescharacteristic
194#394—21no—
195#393—21no—
196#390C2×D4311yescharacteristic
197#387—21no—
198#343—431no—
199#339—861no—
200#328—861no—
201#328—861no—
202#324—431no—
203#324—431no—
204C43#1227611yescharacteristic, complemented, Sylow
205C22×Q8C22⋊D4311yescharacteristic
206C22×D4C22⋊D4311yescharacteristic
207C2×Q16—1721no—
208C2×M16—861no—
209C4⋊Q8—1721no—
210#125—1721no—
211C22⋊Q8—861no—
212C22⋊Q8—861no—
213#117—861no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C22⋊D4311yescharacteristic
218C2×C4⋊C4C22×D4311yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42C22⋊D4311yescharacteristic
226#106—1721no—
227#103—1721no—
228#103—1721no—
229#102—1721no—
230#102—1721no—
231C22⋊C8—861no—
232C22⋊C8—861no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95C22⋊D4311yescharacteristic
239#95C22⋊D4311yescharacteristic
240C24—21no—
241C2×Q8—41no—
242C2×Q8—81no—
243C2×Q8—861no—
244C2×Q8—861no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4C2×C22⋊D4311yescharacteristic
255C22×C4C2×C22⋊D4311yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257Q16—3442no—
258M16—1721no—
259M16—1721no—
260C2×C8—1721no—
261C2×C8—1721no—
262C2×C8—1721no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C22⋊C4—81no—
276C22⋊C4—81no—
277C22⋊C4—81no—
278C22⋊C4—81no—
279C22⋊C4—81no—
280C22⋊C4—81no—
281C22⋊C4—1721no—
282C42—41no—
283C42—1721no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23#1306329411yescharacteristic
292Q8—42no—
293Q8—81no—
294Q8—3441no—
295Q8—3441no—
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—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4#1306334511yescharacteristic
322C2×C4#1306335511yescharacteristic
323C8—3441no—
324C8—3441no—
325C8—3441no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1458306111yescharacteristic
336C22#1458307711yescharacteristic
337C22#1458308611yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—3441no—
348C4—3441no—
349C2—21no—
350C2—21no—
351C2—161no—
352C2#1913357511yescharacteristic
353C2#1913660211yescharacteristic
354C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2830C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
hypercenter#2830D43
hypocenterC43#12276
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2830

Complements

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

NH ≅ G/Ntype
2. #19133602C2semidirect
3. #19133568C2semidirect
4. #19132625C2semidirect
5. #19132601C2semidirect
204. C43#12276semidirect

Maximal subgroups

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

subgroupindex
#191357512
#191336022
#191335682
#191326252
#191326012
#191325272
C43×#28302
#1227643