Finite Group Databasebeta

← #24994050

Subgroups — #24994050

Order 11008.

606 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 99 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#19139753C211yesmaximal, characteristic
2#19137193C211yesmaximal, characteristic
3#19133116C212yesmaximal, complemented
4#19132480C212yesmaximal, complemented
5C43×#1462C211yesmaximal, characteristic
6C2×#13063304C2211yescharacteristic
7#14582824C412yescomplemented
8#14582811C412yescomplemented
9#14582793—22no—
10#14582792—24no—
11#14582762—21no—
12#14582759—21no—
13#14582755—21no—
14#14582755—21no—
15C4×C22⋊Dic43C2211yescharacteristic
16C4×C22⋊Dic43C2212yes—
17#14582637—24no—
18C22×C22⋊C4×C43C2211yescharacteristic
19C43×#407C2212yes—
20C43×#323—22no—
21C22×Dic86C2×C411yescharacteristic
22#13063304—22no—
23#13063304—22no—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43C2×C411yescharacteristic
26C2×Dic43⋊C4—21no—
27C2×C22⋊Dic43—22no—
28C2×C22⋊Dic43—21no—
29C2×C22⋊Dic43—22no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43—22no—
34C2×C4×Dic43—22no—
35C2×C4×Dic43—21no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95C2×C412yes—
40C43⋊#95D414yes—
41C25×C43D411yescharacteristic
42C23×C4×C43D411yescharacteristic
43C23×C4×C43C2311yescharacteristic
44C2×M16×C43—22no—
45C2×C22⋊C4×C43—22no—
46C2×C22⋊C4×C43—22no—
47C2×C22⋊C4×C43C2×C412yes—
48C2×C22⋊C4×C43D412yes—
49C22⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51C24×C43—21no—
52C24×C43—21no—
53C24×C43—42no—
54C24×C43—42no—
55C24×C43—81no—
56C24×C43C22⋊C412yes—
57C24×C43C2×D411yescharacteristic
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—42no—
61C22×C4×C43—81no—
62C22×C4×C43C22⋊C412yes—
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D412yes—
66C22×C4×C43#4112yes—
67C22×Dic43—22no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—24no—
71C2×Dic86—22no—
72C2×Dic86—81no—
73M16×C43—82no—
74C2×C8×C43—42no—
75C22⋊C4×C43—24no—
76C22⋊C4×C43—24no—
77C22⋊Dic43—44no—
78C22⋊Dic43—42no—
79C22⋊Dic43—44no—
80C22⋊Dic43—41no—
81C22⋊Dic43—41no—
82C22⋊Dic43—82no—
83C22⋊Dic43—82no—
84C22⋊Dic43—82no—
85C4⋊Dic43—22no—
86C4⋊Dic43—82no—
87Dic43⋊C4—42no—
88C4×Dic43—82no—
89C4×Dic43—81no—
90C23×C43—22no—
91C23×C43—22no—
92C23×C43—22no—
93C23×C43—22no—
94C23×C43—22no—
95C23×C43—41no—
96C23×C43—42no—
97C23×C43—42no—
98C23×C43—42no—
99C23×C43—42no—
100C23×C43—42no—
101C23×C43—42no—
102C23×C43—81no—
103C23×C43—81no—
104C23×C43—88no—
105C23×C43C2×C22⋊C411yescharacteristic
106C23×C43#12011yescharacteristic
107C23×C43#12311yescharacteristic
108C2×C4×C43—22no—
109C2×C4×C43—42no—
110C2×C4×C43—41no—
111C2×C4×C43—42no—
112C2×C4×C43—41no—
113C2×C4×C43—42no—
114C2×C4×C43—42no—
115C2×C4×C43—81no—
116C2×C4×C43C4×D412yes—
117C2×C4×C43#12112yes—
118C2×Dic43—42no—
119C2×Dic43—44no—
120C2×Dic43—42no—
121C2×Dic43—44no—
122C2×Dic43—42no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—44no—
128Dic86—82no—
129C8×C43—82no—
130#9411—431nomaximal, Sylow
131C22×C43—21no—
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—21no—
138C22×C43—44no—
139C22×C43—44no—
140C22×C43—42no—
141C22×C43—42no—
142C22×C43—42no—
143C22×C43—82no—
144C22×C43—84no—
145C22×C43—84no—
146C22×C43#38611yescharacteristic
147C22×C43#42112yes—
148C22×C43#45512yes—
149C4×C43—22no—
150C4×C43—22no—
151C4×C43—42no—
152Dic43—84no—
153Dic43—82no—
154Dic43—81no—
155Dic43—81no—
156#2561—431no—
157#2312—431no—
158#1508—432no—
159#1462D4311yescharacteristic
160#1297—432no—
161C2×C43—22no—
162C2×C43—22no—
163C2×C43—41no—
164C2×C43—82no—
165C2×C43#188511yescharacteristic
166C2×C43#189711yescharacteristic
167C2×C43#191311yescharacteristic
168C2×C22⋊Q8—431no—
169C22×C22⋊C4C2×D4311yescharacteristic
170#407C2×D4312yes—
171#397—432no—
172#393—432no—
173#388—864no—
174#388—862no—
175#381—861no—
176#380—861no—
177#379—861no—
178#379—861no—
179C4×C22⋊C4—431no—
180C4×C22⋊C4—432no—
181#328—864no—
182#323—22no—
183C43#941111yescharacteristic, complemented, Sylow
184C25D17211yescharacteristic
185C22×Q8—431no—
186C23×C4D17211yescharacteristic
187C23×C4C22×D4311yescharacteristic
188C2×M16—22no—
189C22⋊Q8—862no—
190C22⋊Q8—862no—
191C2×C4⋊C4—431no—
192C2×C4⋊C4—862no—
193C2×C4⋊C4—861no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—862no—
197C2×C22⋊C4—862no—
198C2×C22⋊C4—862no—
199C2×C22⋊C4—862no—
200C2×C22⋊C4—861no—
201C2×C22⋊C4—862no—
202C2×C22⋊C4—861no—
203C2×C22⋊C4C4×D4312yes—
204C2×C22⋊C4C22⋊D4312yes—
205C2×C42—862no—
206C2×C42—861no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209#95—432no—
210#95—434no—
211#95—862no—
212#95—862no—
213#95—862no—
214C24—21no—
215C24—21no—
216C24—42no—
217C24—42no—
218C24—81no—
219C24(C2×D43)⋊C412yes—
220C24C2×D17211yescharacteristic
221C2×Q8—862no—
222C2×Q8—3441no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—42no—
226C22×C4—81no—
227C22×C4—862no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4—864no—
231C22×C4(C2×D43)⋊C412yes—
232C22×C4C2×C4×D4311yescharacteristic
233C22×C4D4×D4312yes—
234C22×C4#1062190012yes—
235C22×C4C2×C22⋊D4311yescharacteristic
236M16—82no—
237C2×C8—42no—
238C4⋊C4—862no—
239C4⋊C4—3442no—
240C4⋊C4—1722no—
241C22⋊C4—24no—
242C22⋊C4—24no—
243C22⋊C4—3442no—
244C22⋊C4—3442no—
245C22⋊C4—3442no—
246C22⋊C4—1722no—
247C22⋊C4—1724no—
248C22⋊C4—1724no—
249C22⋊C4—1721no—
250C22⋊C4—1721no—
251C42—3442no—
252C42—3441no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—41no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—81no—
266C23—81no—
267C23—88no—
268C23C2×(C2×D43)⋊C411yescharacteristic
269C23#1306329511yescharacteristic
270C23#1306330911yescharacteristic
271Q8—3442no—
272C2×C4—22no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—81no—
280C2×C4—1722no—
281C2×C4—1724no—
282C2×C4—1722no—
283C2×C4—1722no—
284C2×C4—1724no—
285C2×C4—1724no—
286C2×C4—1722no—
287C2×C4—1722no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4(C22⋊D43)⋊C412yes—
291C2×C4#1306329712yes—
292C8—82no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—44no—
301C22—44no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—82no—
306C22—84no—
307C22—84no—
308C22#1458277611yescharacteristic
309C22#1458291512yes—
310C22#1458307912yes—
311C4—22no—
312C4—22no—
313C4—42no—
314C4—3444no—
315C4—3442no—
316C4—3441no—
317C4—3441no—
318C2—22no—
319C2—22no—
320C2—41no—
321C2—82no—
322C2#1913498111yescharacteristic
323C2#1913504111yescharacteristic
324C2#1913513511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1462C2
socleC22×C43#386
prime radicalC25×C43D4
cosocleC23×C4×C43C23
hypercenter#1462D43
hypocenterC43#9411
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
3. #19133116C2semidirect
4. #19132480C2semidirect
7. #14582824C4semidirect
8. #14582811C4semidirect
183. C43#9411semidirect

Maximal subgroups

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

subgroupindex
#191397532
#191371932
#191331162
#191324802
C43×#14622
#941143