Finite Group Databasebeta

← #24992120

Subgroups — #24992120

Order 11008.

602 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 115 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#19143636C211yesmaximal, characteristic, complemented
2#19137317C211yesmaximal, characteristic
3#19132985C212yesmaximal, complemented
4#19132423C212yesmaximal, complemented
5C43×#1460C211yesmaximal, characteristic, complemented
6C2×#13063321C411yescharacteristic
7C2×C4×D172C2211yescharacteristic
8#14582977—24no—
9#14582952C2212yes—
10#14582863—22no—
11#14582802C411yescharacteristic
12#14582800C411yescharacteristic
13#14582778—22no—
14#14582775—22no—
15#14582764C411yescharacteristic
16#14582745C2211yescharacteristic
17#14582626—24no—
18C2×C4×D4×C43C2211yescharacteristic
19C43×#431C2212yes—
20C43×#323—22no—
21C22×D172C2×C411yescharacteristic
22C22×C22⋊D43—22no—
23C22×C4×D43—21no—
24C2×#10621877—24no—
25#13063321—22no—
26#13063321—22no—
27C4×D172—22no—
28C4×D172—22no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×C22⋊Dic43—22no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—22no—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43C2×C411yescharacteristic
35C4⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)—24no—
37C22⋊(C43⋊C8)—22no—
38C4×C43⋊C8D414yescomplemented
39C43⋊#95—22no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C22×D4×C43C2×C411yescharacteristic
43C23×C4×C43D412yes—
44C4×D4×C43—22no—
45C4×D4×C43—22no—
46C2×C4⋊C4×C43C2×C411yescharacteristic
47C2×C22⋊C4×C43D412yes—
48C2×C42×C43C2311yescharacteristic
49C4⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51C4×C8×C43—22no—
52C24×C43C22⋊C412yes—
53C23×D43—21no—
54C2×D4×C43—22no—
55C2×D4×C43—21no—
56C2×D4×C43—21no—
57C2×D4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—82no—
61C22×C4×C43C22⋊C412yes—
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C2×C22⋊D43—28no—
66C2×C22⋊D43—82no—
67C2×C22⋊D43—82no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×D172—21no—
72C2×D172—22no—
73C2×D172—22no—
74C2×D172M1612yescomplemented
75C2×C4×D43—42no—
76C2×C4×D43—82no—
77C2×C8×C43—42no—
78C4⋊C4×C43—22no—
79C22⋊C4×C43—24no—
80C42×C43C2×D412yes—
81C42×C43#4112yes—
82C22⋊Dic43—82no—
83(C2×D43)⋊C4—41no—
84(C2×D43)⋊C4—41no—
85(C2×D43)⋊C4—82no—
86C4⋊Dic43—22no—
87C4×Dic43—21no—
88C4×Dic43—22no—
89C4×Dic43M1612yescomplemented
90#10621877—84no—
91C2×C43⋊C8—24no—
92C23×C43—22no—
93C23×C43—22no—
94C23×C43—22no—
95C23×C43—42no—
96C23×C43—42no—
97C23×C43C2×C22⋊C411yescharacteristic
98C22×D43—22no—
99C22×D43—42no—
100C22×D43—42no—
101C22×D43—41no—
102C22×D43—41no—
103D4×C43—42no—
104D4×C43—42no—
105C2×C4×C43—22no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—44no—
109C2×C4×C43—42no—
110C2×C4×C43—82no—
111C2×C4×C43C4×D412yes—
112C2×C4×C43#12011yescharacteristic
113C2×C4×C43#12112yes—
114C2×C4×C43#12311yescharacteristic
115C2×C4×C43C2×M1611yescharacteristic
116C2×C4×C43C2×M1611yescharacteristic
117C2×C4×C43#13112yes—
118C22⋊D43—88no—
119C2×Dic43—22no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—42no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127D172—24no—
128D172—42no—
129C4×D43—84no—
130C8×C43—82no—
131C43⋊C8—44no—
132#9105—431nomaximal, Sylow
133C22×C43—21no—
134C22×C43—21no—
135C22×C43—44no—
136C22×C43—42no—
137C22×C43—42no—
138C22×C43—42no—
139C22×C43—82no—
140C22×C43#38611yescharacteristic
141C22×C43#40711yescharacteristic
142C22×C43#40811yescharacteristic
143C2×D43—44no—
144C2×D43—42no—
145C2×D43—82no—
146C2×D43—81no—
147C2×D43—81no—
148C4×C43—22no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—42no—
152C4×C43#43512yes—
153C4×C43#43612yes—
154Dic43—42no—
155Dic43—81no—
156Dic43—81no—
157#2975—431no—
158#2328—431no—
159#1478—432no—
160#1460D4311yescharacteristic, complemented
161#1274—432no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43—82no—
165C2×C43#187011yescharacteristic
166C2×C43#191011yescharacteristic
167C2×C43#191111yescharacteristic
168D43—82no—
169C2×#127—431no—
170C2×C4×D4—431no—
171C2×C4×D4C2×D4311yescharacteristic
172#436—864no—
173#431—432no—
174#431C2×D4312yes—
175#407—862no—
176#390—431no—
177#390—431no—
178#386—862no—
179#386—862no—
180#382—431no—
181#376—431no—
182D4⋊C8—864no—
183#323—22no—
184C43#910511yescharacteristic, complemented, Sylow
185C22×D4—431no—
186C22×D4—862no—
187C22×D4C4×D4311yescharacteristic
188C23×C4—861no—
189C23×C4D17212yes—
190C2×M16—864no—
191#127—862no—
192#127—862no—
193C4×D4—22no—
194C4×D4—22no—
195C4×D4—862no—
196C4×D4—862no—
197C2×C4⋊C4—431no—
198C2×C4⋊C4C4×D4311yescharacteristic
199C2×C22⋊C4—862no—
200C2×C22⋊C4—862no—
201C2×C22⋊C4—861no—
202C2×C22⋊C4C22⋊D4312yes—
203C2×C42—431no—
204C2×C42—431no—
205C2×C42C22×D4311yescharacteristic
206C4⋊C8—22no—
207C4⋊C8—862no—
208C22⋊C8—22no—
209C22⋊C8—864no—
210C22⋊C8—862no—
211C4×C8—22no—
212C4×C8—434no—
213#95—862no—
214#95—861no—
215#95—861no—
216C24—861no—
217C24(C2×D43)⋊C412yes—
218C2×D4—22no—
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—22no—
222C2×D4—432no—
223C2×D4—868no—
224C2×D4—862no—
225C2×D4—861no—
226C2×D4—862no—
227C2×D4—3442no—
228C2×D4—3442no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—82no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4—3442no—
236C22×C4—1722no—
237C22×C4(C2×D43)⋊C412yes—
238C22×C4C2×C4×D4311yescharacteristic
239C22×C4C2×D17211yescharacteristic
240C22×C4C2×C22⋊D4311yescharacteristic
241M16—3444no—
242C2×C8—42no—
243C2×C8—864no—
244C4⋊C4—22no—
245C4⋊C4—862no—
246C22⋊C4—24no—
247C22⋊C4—3442no—
248C22⋊C4—3442no—
249C22⋊C4—1721no—
250C22⋊C4—1721no—
251C42—432no—
252C42—861no—
253C42—862no—
254C42D4×D4312yes—
255C42#1062190012yes—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—42no—
260C23—42no—
261C23—862no—
262C23—1722no—
263C23—1722no—
264C23—1721no—
265C23—1721no—
266C23C2×(C2×D43)⋊C411yescharacteristic
267D4—42no—
268D4—42no—
269D4—864no—
270D4—3448no—
271D4—1722no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—82no—
278C2×C4—862no—
279C2×C4—3444no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4—1722no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4(C22⋊D43)⋊C412yes—
288C2×C4#1306329511yescharacteristic
289C2×C4#1306329712yes—
290C2×C4#1306330911yescharacteristic
291C2×C4M16×D4311yescharacteristic
292C2×C4M16×D4311yescharacteristic
293C2×C4#1306333112yes—
294C8—82no—
295C8—1724no—
296C22—21no—
297C22—21no—
298C22—44no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—82no—
303C22—3442no—
304C22—3441no—
305C22—3441no—
306C22—1724no—
307C22—1722no—
308C22#1458277611yescharacteristic
309C22#1458286211yescharacteristic
310C22#1458286511yescharacteristic
311C4—22no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—3441no—
316C4—3441no—
317C4—1722no—
318C4#1458297312yes—
319C4#1458297412yes—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—3442no—
324C2#1913489011yescharacteristic
325C2#1913512011yescharacteristic
326C2#1913512511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1460C2
socleC22×C43#386
prime radicalC2×#13063321C4
cosocleC2×C42×C43C23
hypercenter#1460D43
hypocenterC43#9105
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
1. #19143636C2semidirect
3. #19132985C2semidirect
4. #19132423C2semidirect
5. C43×#1460C2semidirect
38. C4×C43⋊C8D4semidirect
74. C2×D172M16semidirect
89. C4×Dic43M16semidirect
160. #1460D43semidirect
184. C43#9105semidirect

Maximal subgroups

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

subgroupindex
#191436362
#191373172
#191329852
#191324232
C43×#14602
#910543