Finite Group Databasebeta

← #24985101

Subgroups — #24985101

Order 11008.

444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 107 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#19142962C211yesmaximal, characteristic
2#19134344C211yesmaximal, characteristic, complemented
3#19132419C212yesmaximal, complemented
4#19132415C212yesmaximal
5C43×#1744C211yesmaximal, characteristic, complemented
6C2×#13063319—21no—
7C2×#13063236—21no—
8#14582801C411yescharacteristic
9#14582801C411yescharacteristic
10#14582801C2211yescharacteristic
11#14582797C411yescharacteristic
12#14582797C411yescharacteristic
13#14582797C2211yescharacteristic
14#14582790—21no—
15#14582790—21no—
16#14582790—21no—
17#14582654—21no—
18#14582654C2212yes—
19C2×C4×C8×C43—21no—
20C43×C43C2211yescharacteristic
21C43×#336—21no—
22C43×#336C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C43⋊C8—22no—
25#13063319—44no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38#13063236—24no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C22×C8×C43—22no—
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43C2×C411yescharacteristic
45C2×C42×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C2×C42×C43D411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43C2311yescharacteristic
50C4×C8×C43—24no—
51C23×D43—21no—
52C22×C4×C43C22⋊C411yescharacteristic
53C22×C4×C43C22⋊C411yescharacteristic
54C22×C4×C43C22⋊C411yescharacteristic
55C22×C4×C43C22⋊C411yescharacteristic
56C22×C4×C43C22×C411yescharacteristic
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×Dic43—21no—
60C22×Dic43—21no—
61C22×Dic43—21no—
62C2×D172—22no—
63C2×D172—41no—
64C2×D172—41no—
65C2×C8×C43—24no—
66C2×C8×C43—42no—
67C2×C8×C43—42no—
68C42×C43—22no—
69C42×C43—22no—
70C42×C43—22no—
71C42×C43—22no—
72C42×C43—22no—
73C42×C43—41no—
74C42×C43—41no—
75(C2×D43)⋊C4—42no—
76(C2×D43)⋊C4—42no—
77(C2×D43)⋊C4—42no—
78(C2×D43)⋊C4—42no—
79(C2×D43)⋊C4—42no—
80(C2×D43)⋊C4—42no—
81C4⋊Dic43—22no—
82C4⋊Dic43—41no—
83C4⋊Dic43—41no—
84Dic43⋊C4—42no—
85Dic43⋊C4—42no—
86Dic43⋊C4—42no—
87C2×C43⋊C8—24no—
88C2×C43⋊C8—42no—
89C2×C43⋊C8—42no—
90C23×C43C2×C22⋊C411yescharacteristic
91C22×D43—41no—
92C22×D43—41no—
93C22×D43—41no—
94C22×D43—41no—
95C22×D43—41no—
96C22×D43—41no—
97C22×D43—41no—
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—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43#10412yes—
115C2×C4×C43#10412yes—
116C2×C4×C43#13112yes—
117C2×C4×C43#13512yes—
118C2×C4×C43AGL(1,ℤ/8)12yes—
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—
128D172—82no—
129C8×C43—44no—
130C43⋊C8—44no—
131#7692—431nomaximal, Sylow
132C22×C43#40811yescharacteristic
133C22×C43#41011yescharacteristic
134C22×C43#41311yescharacteristic
135C22×C43#41611yescharacteristic
136C22×C43#41811yescharacteristic
137C22×C43C2×#10411yescharacteristic
138C22×C43C2×#10411yescharacteristic
139C2×D43—81no—
140C2×D43—81no—
141C2×D43—81no—
142C2×D43—81no—
143C2×D43—81no—
144C2×D43—81no—
145C2×D43—81no—
146C4×C43—22no—
147C4×C43—22no—
148C4×C43—22no—
149C4×C43—22no—
150C4×C43—22no—
151C4×C43—41no—
152C4×C43—41no—
153Dic43—81no—
154Dic43—81no—
155Dic43—81no—
156#2860—431no—
157#1745—431no—
158#1744D4311yescharacteristic, complemented
159#1271—432no—
160#1270—432no—
161C2×C43#147311yescharacteristic
162C2×C43#148411yescharacteristic
163C2×C43#149411yescharacteristic
164C2×C43#150011yescharacteristic
165C2×C43#150511yescharacteristic
166C2×C43#152411yescharacteristic
167C2×C43#155311yescharacteristic
168D43—161no—
169C2×#126—861no—
170C2×#97—861no—
171C2×C4×C8—21no—
172#390—431no—
173#390—431no—
174#390—431no—
175#389—431no—
176#389—431no—
177#389—431no—
178#388—861no—
179#388—861no—
180#388—861no—
181C43C2×D4311yescharacteristic
182#336—21no—
183#336—432no—
184#336—861no—
185#336C2×D4312yes—
186C43#769211yescharacteristic, complemented, Sylow
187C22×D4—431no—
188C22×C8—22no—
189C22×C8—862no—
190#126—1724no—
191C2×C4⋊C4—431no—
192C2×C4⋊C4—431no—
193C2×C4⋊C4—431no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—861no—
196C2×C4⋊C4—861no—
197C2×C22⋊C4—861no—
198C2×C22⋊C4—861no—
199C2×C22⋊C4—861no—
200C2×C22⋊C4—861no—
201C2×C22⋊C4—861no—
202C2×C22⋊C4—861no—
203C2×C42C4×D4311yescharacteristic
204C2×C42C4×D4311yescharacteristic
205C2×C42D17211yescharacteristic
206C2×C42D17211yescharacteristic
207C2×C42C22⋊D4311yescharacteristic
208C2×C42C22⋊D4311yescharacteristic
209C2×C42C22×D4311yescharacteristic
210#97—864no—
211C4×C8—24no—
212#95—861no—
213#95—861no—
214#95—861no—
215C24—861no—
216C2×D4—862no—
217C2×D4—1721no—
218C2×D4—1721no—
219C22×C4—861no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4(C2×D43)⋊C411yescharacteristic
223C22×C4(C2×D43)⋊C411yescharacteristic
224C22×C4(C2×D43)⋊C411yescharacteristic
225C22×C4(C2×D43)⋊C411yescharacteristic
226C22×C4C2×C4×D4311yescharacteristic
227C22×C4C2×D17211yescharacteristic
228C22×C4C2×C22⋊D4311yescharacteristic
229C2×C8—24no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—864no—
233C2×C8—1722no—
234C2×C8—1722no—
235C4⋊C4—862no—
236C4⋊C4—1721no—
237C4⋊C4—1721no—
238C4⋊C4—1722no—
239C4⋊C4—1722no—
240C4⋊C4—1722no—
241C22⋊C4—1722no—
242C22⋊C4—1722no—
243C22⋊C4—1722no—
244C22⋊C4—1722no—
245C22⋊C4—1722no—
246C22⋊C4—1722no—
247C42—22no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—22no—
252C42—41no—
253C42—41no—
254C23—1721no—
255C23—1721no—
256C23—1721no—
257C23—1721no—
258C23—1721no—
259C23—1721no—
260C23—1721no—
261C23C2×(C2×D43)⋊C411yescharacteristic
262D4—3442no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
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—1721no—
288C2×C4#1306325112yes—
289C2×C4#1306325312yes—
290C2×C4#1306333112yes—
291C2×C4#1306334712yes—
292C2×C4#1306335012yes—
293C8—44no—
294C8—1724no—
295C22—3441no—
296C22—3441no—
297C22—3441no—
298C22—3441no—
299C22—3441no—
300C22—3441no—
301C22—3441no—
302C22#1458286511yescharacteristic
303C22#1458287211yescharacteristic
304C22#1458288111yescharacteristic
305C22#1458289611yescharacteristic
306C22#1458290311yescharacteristic
307C22C2×#1306325111yescharacteristic
308C22C2×#1306325311yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—3441no—
317C4—3441no—
318C4—3441no—
319C2—6881no—
320C2#1913296211yescharacteristic
321C2#1913301111yescharacteristic
322C2#1913305611yescharacteristic
323C2#1913308211yescharacteristic
324C2#1913310211yescharacteristic
325C2#1913318111yescharacteristic
326C2#1913329811yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1744C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1744D43
hypocenterC43#7692
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ #1744

Complements

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

NH ≅ G/Ntype
2. #19134344C2semidirect
3. #19132419C2semidirect
5. C43×#1744C2semidirect
158. #1744D43semidirect
186. C43#7692semidirect

Maximal subgroups

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

subgroupindex
#191429622
#191343442
#191324192
#191324152
C43×#17442
#769243