Finite Group Databasebeta

← #24984824

Subgroups — #24984824

Order 11008.

594 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#14582797C211yesmaximal, characteristic
2#19134357C211yesmaximal, characteristic
3#19132419C214yesmaximal, complemented
4C43×#1749C211yesmaximal, characteristic
5C22×C4⋊Dic43C411yescharacteristic
6C22×C4⋊Dic43C411yescharacteristic
7C22×Dic43⋊C4—21no—
8C2×C22⋊(C43⋊C8)—21no—
9C2×#13063236—21no—
10#14582797—21no—
11#14582797—21no—
12#14582797C412yes—
13#14582797C2212yes—
14C2×C43⋊#95—21no—
15#14582654C2212yes—
16C22×C42×C43C2211yescharacteristic
17C2×C22⋊C8×C43—21no—
18C2×#97×C43—21no—
19C43×#336C2212yes—
20C23×Dic43—21no—
21C23×Dic43—21no—
22C22×C43⋊C8—22no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—24no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43—42no—
27C2×C4⋊Dic43C2×C412yes—
28C2×C4⋊Dic43C2×C412yes—
29C2×Dic43⋊C4—22no—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—44no—
32C22⋊(C43⋊C8)—24no—
33#13063236—42no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C23×C4×C43C2×C411yescharacteristic
37C23×C4×C43D411yescharacteristic
38C23×C4×C43D411yescharacteristic
39C22×C8×C43—22no—
40C2×C42×C43—42no—
41C2×C42×C43C2×C411yescharacteristic
42C2×C42×C43D411yescharacteristic
43C2×C42×C43D411yescharacteristic
44C2×C42×C43C2311yescharacteristic
45C22⋊C8×C43—24no—
46#97×C43—42no—
47C24×C43C22⋊C411yescharacteristic
48C22×C4×C43—22no—
49C22×C4×C43—22no—
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—41no—
56C22×C4×C43—41no—
57C22×C4×C43C22⋊C411yescharacteristic
58C22×C4×C43C22⋊C411yescharacteristic
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43C22×C411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D411yescharacteristic
63C22×Dic43—24no—
64C22×Dic43—22no—
65C22×Dic43—22no—
66C22×Dic43—42no—
67C22×Dic43—42no—
68C22×Dic43—42no—
69C22×Dic43—42no—
70C22×Dic43—42no—
71C2×C8×C43—24no—
72C2×C8×C43—42no—
73C2×C8×C43—42no—
74C42×C43—22no—
75C42×C43—22no—
76C42×C43—41no—
77C42×C43—41no—
78C4⋊Dic43—24no—
79C4⋊Dic43—22no—
80C4⋊Dic43—42no—
81C4⋊Dic43—42no—
82C4⋊Dic43M1614yes—
83Dic43⋊C4—44no—
84Dic43⋊C4—44no—
85C2×C43⋊C8—24no—
86C2×C43⋊C8—42no—
87C2×C43⋊C8—42no—
88C23×C43—21no—
89C23×C43—21no—
90C23×C43—21no—
91C23×C43—21no—
92C23×C43#10112yes—
93C23×C43#10412yes—
94C23×C43#10412yes—
95C23×C43C2×C22⋊C411yescharacteristic
96C2×C4×C43—28no—
97C2×C4×C43—21no—
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—44no—
112C2×C4×C43—44no—
113C2×C4×C43#9912yes—
114C2×C4×C43C2×M1612yes—
115C2×C4×C43AGL(1,ℤ/8)12yes—
116C2×C4×C43#13712yes—
117C2×Dic43—24no—
118C2×Dic43—48no—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123C2×Dic43—42no—
124C2×Dic43—84no—
125C8×C43—44no—
126C43⋊C8—44no—
127#7627—431nomaximal, Sylow
128C22×C43—22no—
129C22×C43—22no—
130C22×C43—22no—
131C22×C43—22no—
132C22×C43—22no—
133C22×C43—22no—
134C22×C43#33014yes—
135C22×C43#40711yescharacteristic
136C22×C43C2×#9911yescharacteristic
137C22×C43C2×#10111yescharacteristic
138C22×C43#41811yescharacteristic
139C22×C43#41911yescharacteristic
140C22×C43C2×#10411yescharacteristic
141C22×C43C2×#10411yescharacteristic
142C4×C43—22no—
143C4×C43—22no—
144C4×C43—22no—
145C4×C43—22no—
146C4×C43—41no—
147C4×C43—41no—
148Dic43—44no—
149Dic43—82no—
150C2×#389—431no—
151#1749—431no—
152#1749D4311yescharacteristic
153#1271—434no—
154C2×C43—24no—
155C2×C43#146311yescharacteristic
156C2×C43#149011yescharacteristic
157C2×C43#149111yescharacteristic
158C2×C43#150711yescharacteristic
159C2×C43#150811yescharacteristic
160C2×C43C2×#33011yescharacteristic
161C2×C43#155611yescharacteristic
162C22×C4⋊C4—431no—
163C22×C4⋊C4—431no—
164C22×C4⋊C4—861no—
165C22×C42C2×D4311yescharacteristic
166C2×C22⋊C8—21no—
167C2×C22⋊C8—861no—
168C2×#97—21no—
169C2×#97—861no—
170#389—432no—
171#389—432no—
172#389—861no—
173#389—861no—
174C2×#95—861no—
175#336—432no—
176#336C2×D4312yes—
177C43#762711yescharacteristic, complemented, Sylow
178C23×C4—861no—
179C23×C4—861no—
180C23×C4C4×D4311yescharacteristic
181C23×C4D17211yescharacteristic
182C23×C4C22⋊D4311yescharacteristic
183C22×C8—22no—
184C22×C8—862no—
185C2×C4⋊C4—432no—
186C2×C4⋊C4—432no—
187C2×C4⋊C4—864no—
188C2×C4⋊C4—861no—
189C2×C4⋊C4—861no—
190C2×C4⋊C4—862no—
191C2×C4⋊C4—862no—
192C2×C4⋊C4—1724no—
193C2×C4⋊C4—1722no—
194C2×C42—42no—
195C2×C42C4×D4311yescharacteristic
196C2×C42D17211yescharacteristic
197C2×C42C22⋊D4311yescharacteristic
198C2×C42C22×D4311yescharacteristic
199C22⋊C8—24no—
200C22⋊C8—864no—
201#97—42no—
202#97—1722no—
203#95—862no—
204#95—862no—
205C24(C2×D43)⋊C411yescharacteristic
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—864no—
216C22×C4—862no—
217C22×C4—862no—
218C22×C4—1722no—
219C22×C4—1722no—
220C22×C4—1722no—
221C22×C4—1722no—
222C22×C4—1722no—
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—434no—
236C4⋊C4—864no—
237C4⋊C4—862no—
238C4⋊C4—1722no—
239C4⋊C4—1724no—
240C4⋊C4—1722no—
241C4⋊C4—1724no—
242C42—22no—
243C42—22no—
244C42—41no—
245C42—41no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23#1306324312yes—
251C23#1306325112yes—
252C23#1306325312yes—
253C23C2×(C2×D43)⋊C411yescharacteristic
254C2×C4—28no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—864no—
272C2×C4—3444no—
273C2×C4—1722no—
274C2×C4—1722no—
275C2×C4—1722no—
276C2×C4—1728no—
277C2×C4—1722no—
278C2×C4—1722no—
279C2×C4#1306323912yes—
280C2×C4M16×D4312yes—
281C2×C4#1306335012yes—
282C2×C4#1306335812yes—
283C8—44no—
284C8—1724no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22#1458264014yes—
292C22#1458286211yescharacteristic
293C22C2×#1306323911yescharacteristic
294C22C2×#1306324311yescharacteristic
295C22#1458290311yescharacteristic
296C22#1458290911yescharacteristic
297C22C2×#1306325111yescharacteristic
298C22C2×#1306325311yescharacteristic
299C4—22no—
300C4—22no—
301C4—22no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—3442no—
306C4—1724no—
307C2—24no—
308C2#1913292411yescharacteristic
309C2#1913303711yescharacteristic
310C2#1913304311yescharacteristic
311C2#1913311011yescharacteristic
312C2#1913311611yescharacteristic
313C2C2×#1458264011yescharacteristic
314C2#1913331311yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1749C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1749D43
hypocenterC43#7627
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. #19132419C2semidirect
177. C43#7627semidirect

Maximal subgroups

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

subgroupindex
C2×#145827972
#191343572
#191324192
C43×#17492
#762743