Finite Group Databasebeta

← #24989205

Subgroups — #24989205

Order 11008.

1266 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C22×#13063306C211yesmaximal, characteristic
2#19134667C214yesmaximal, complemented
3#19134510C211yesmaximal, characteristic
4C43×#1781C211yesmaximal, characteristic
5C24×Dic43C411yescharacteristic, complemented
6C2×#13063306—28no—
7C2×#13063306—22no—
8C2×#13063306—22no—
9C22×Dic43⋊C4C412yescomplemented
10C22×C22⋊Dic43C411yescharacteristic, complemented
11C22×C22⋊Dic43C2212yes—
12C2×#13063240—22no—
13#14582755C2212yes—
14#14582665—28no—
15C23×D4×C43C2211yescharacteristic
16C2×#99×C43—22no—
17C43×#379C2212yes—
18C23×Dic43—22no—
19C23×Dic43—24no—
20C23×Dic43—44no—
21C23×Dic43C2×C412yes—
22C23×Dic43C2×C412yes—
23#13063306—216no—
24#13063306—216no—
25C2×Dic43⋊C4—24no—
26C2×Dic43⋊C4—24no—
27C2×Dic43⋊C4—24no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—22no—
30C2×C22⋊Dic43—24no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—24no—
33C2×C22⋊Dic43—22no—
34C2×C22⋊Dic43—24no—
35C2×C22⋊Dic43D418yes—
36#13063240—44no—
37C25×C43C2×C411yescharacteristic
38C25×C43C2311yescharacteristic
39C22×D4×C43—24no—
40C22×D4×C43—44no—
41C22×D4×C43D412yes—
42C22×D4×C43D412yes—
43C23×C4×C43C2×C411yescharacteristic
44C2×C22⋊C4×C43—24no—
45C2×C22⋊C4×C43—22no—
46#99×C43—44no—
47C24×C43—24no—
48C24×C43—22no—
49C24×C43—42no—
50C24×C43—44no—
51C24×C43—44no—
52C24×C43C22⋊C412yes—
53C24×C43C22×C411yescharacteristic
54C24×C43C2×D411yescharacteristic
55C24×C43C2×D414yes—
56C24×C43C2×D411yescharacteristic
57C2×D4×C43—24no—
58C2×D4×C43—24no—
59C2×D4×C43—24no—
60C2×D4×C43—24no—
61C2×D4×C43—42no—
62C2×D4×C43—42no—
63C2×D4×C43—416no—
64C22×C4×C43—22no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43C22⋊C412yes—
68C22×Dic43—28no—
69C22×Dic43—22no—
70C22×Dic43—22no—
71C22×Dic43—22no—
72C22×Dic43—22no—
73C22×Dic43—44no—
74C22×Dic43—44no—
75C22×Dic43—416no—
76C22×Dic43—44no—
77C22×Dic43—44no—
78C22×Dic43—42no—
79C22×Dic43C22⋊C414yes—
80C22×Dic43C22⋊C414yes—
81C22⋊C4×C43—44no—
82C22⋊C4×C43—48no—
83C22⋊Dic43—28no—
84C22⋊Dic43—28no—
85C22⋊Dic43—28no—
86C22⋊Dic43—44no—
87C22⋊Dic43—48no—
88Dic43⋊C4—216no—
89C23×C43—22no—
90C23×C43—24no—
91C23×C43—28no—
92C23×C43—22no—
93C23×C43—22no—
94C23×C43—22no—
95C23×C43—22no—
96C23×C43—28no—
97C23×C43—44no—
98C23×C43—42no—
99C23×C43—44no—
100C23×C43—42no—
101C23×C43—44no—
102C23×C43—416no—
103C23×C43—44no—
104C23×C43—44no—
105C23×C43—88no—
106C23×C43#9914yes—
107C23×C43C2×C22⋊C412yes—
108C23×C43C2×C22⋊C411yescharacteristic
109C23×C43#12012yes—
110C23×C43#12012yes—
111D4×C43—48no—
112D4×C43—48no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—44no—
117C2×C4×C43—82no—
118C2×C4×C43—84no—
119C2×Dic43—24no—
120C2×Dic43—24no—
121C2×Dic43—44no—
122C2×Dic43—44no—
123C2×Dic43—416no—
124C2×Dic43—44no—
125C2×Dic43—44no—
126C2×Dic43—44no—
127C2×Dic43—44no—
128C2×Dic43—82no—
129C2×Dic43—84no—
130#8543—431nomaximal, Sylow
131C22×C43—28no—
132C22×C43—22no—
133C22×C43—22no—
134C22×C43—22no—
135C22×C43—24no—
136C22×C43—22no—
137C22×C43—22no—
138C22×C43—24no—
139C22×C43—24no—
140C22×C43—44no—
141C22×C43—44no—
142C22×C43—416no—
143C22×C43—44no—
144C22×C43—82no—
145C22×C43—82no—
146C22×C43—88no—
147C22×C43#37911yescharacteristic
148C22×C43C2×#9912yes—
149C22×C43#41014yes—
150C4×C43—42no—
151C4×C43—162no—
152Dic43—44no—
153Dic43—44no—
154Dic43—162no—
155C22×#123—431no—
156#1819—434no—
157#1781—431no—
158#1781D4311yescharacteristic
159C2×C43—22no—
160C2×C43—24no—
161C2×C43—42no—
162C2×C43—42no—
163C2×C43—44no—
164C2×C43#178111yescharacteristic
165C2×C43#178212yes—
166C23×D4C2×D4311yescharacteristic
167C24×C4—431no—
168C2×#123—868no—
169C2×#123—862no—
170C2×#123—862no—
171C22×C4⋊C4—432no—
172C22×C22⋊C4—432no—
173C22×C22⋊C4—431no—
174C2×#99—22no—
175C2×#99—862no—
176#379—432no—
177#379C2×D4312yes—
178#342—868no—
179C43#854311yescharacteristic, complemented, Sylow
180C25C4×D4311yescharacteristic
181C25C22×D4311yescharacteristic
182C22×D4—24no—
183C22×D4—44no—
184C22×D4D17212yes—
185C22×D4C22⋊D4312yes—
186C23×C4—432no—
187C23×C4—432no—
188C23×C4—864no—
189C23×C4—862no—
190C23×C4—1724no—
191C23×C4C4×D4311yescharacteristic
192#123—8616no—
193#123—8616no—
194C2×C4⋊C4—864no—
195C2×C4⋊C4—864no—
196C2×C4⋊C4—864no—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—438no—
200C2×C22⋊C4—864no—
201C2×C22⋊C4—862no—
202C2×C22⋊C4—862no—
203C2×C22⋊C4—864no—
204C2×C22⋊C4—862no—
205C2×C22⋊C4—862no—
206C2×C22⋊C4—864no—
207#99—44no—
208#99—1724no—
209C24—24no—
210C24—22no—
211C24—42no—
212C24—44no—
213C24—44no—
214C24(C2×D43)⋊C412yes—
215C24C2×C4×D4311yescharacteristic
216C24C2×D17211yescharacteristic
217C24D4×D4314yes—
218C24C2×C22⋊D4311yescharacteristic
219C2×D4—24no—
220C2×D4—24no—
221C2×D4—24no—
222C2×D4—24no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—416no—
226C22×C4—22no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—434no—
230C22×C4—434no—
231C22×C4—868no—
232C22×C4—862no—
233C22×C4—862no—
234C22×C4—862no—
235C22×C4—862no—
236C22×C4—1722no—
237C22×C4—17216no—
238C22×C4—1724no—
239C22×C4—1724no—
240C22×C4—1724no—
241C22×C4—1724no—
242C22×C4(C2×D43)⋊C412yes—
243C4⋊C4—8616no—
244C22⋊C4—44no—
245C22⋊C4—48no—
246C22⋊C4—868no—
247C22⋊C4—868no—
248C22⋊C4—868no—
249C22⋊C4—1724no—
250C22⋊C4—1728no—
251C23—22no—
252C23—24no—
253C23—28no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—28no—
259C23—44no—
260C23—42no—
261C23—44no—
262C23—42no—
263C23—44no—
264C23—416no—
265C23—44no—
266C23—44no—
267C23—88no—
268C23#1306323914yes—
269C23C22⋊C4×D4312yes—
270C23C2×(C2×D43)⋊C411yescharacteristic
271C23#1306329312yes—
272C23#1306329512yes—
273D4—48no—
274D4—48no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—44no—
279C2×C4—82no—
280C2×C4—84no—
281C2×C4—864no—
282C2×C4—864no—
283C2×C4—3442no—
284C2×C4—3444no—
285C2×C4—1724no—
286C2×C4—17216no—
287C2×C4—1724no—
288C2×C4—1724no—
289C2×C4—1724no—
290C2×C4—1724no—
291C2×C4—1724no—
292C22—28no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—24no—
299C22—24no—
300C22—24no—
301C22—44no—
302C22—44no—
303C22—416no—
304C22—44no—
305C22—82no—
306C22—82no—
307C22—88no—
308C22#1458275411yescharacteristic
309C22C2×#1306323912yes—
310C22#1458287114yes—
311C4—42no—
312C4—162no—
313C4—1724no—
314C4—1724no—
315C4—6882no—
316C2—22no—
317C2—24no—
318C2—42no—
319C2—42no—
320C2—44no—
321C2#1913450911yescharacteristic
322C2#1913451112yes—
subgroupG/H
centerC22#14582754
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC43×#1781C2
socleC22×C43#379
prime radicalC23×D4×C43C22
cosocleC25×C43C23
hypercenter#1781D43
hypocenterC43#8543
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #1781

Complements

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

NH ≅ G/Ntype
2. #19134667C2semidirect
5. C24×Dic43C4semidirect
9. C22×Dic43⋊C4C4semidirect
10. C22×C22⋊Dic43C4semidirect
179. C43#8543semidirect

Maximal subgroups

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

subgroupindex
C22×#130633062
#191346672
#191345102
C43×#17812
#854343