Finite Group Databasebeta

← #24992380

Subgroups — #24992380

Order 11008.

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

normal subgroups only

This group has 648 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
1#19142926C211yesmaximal, characteristic
2C2×#14582767C211yesmaximal, characteristic, complemented
3C2×#14582634C212yesmaximal
4#19132475C212yesmaximal, complemented
5C43×#1817C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063299C2211yescharacteristic
8#14582801C412yescomplemented
9#14582797C412yescomplemented
10#14582790—22no—
11#14582778—21no—
12#14582767—24no—
13#14582759C2211yescharacteristic
14C2×C43⋊#95—21no—
15C2×C43⋊#95—21no—
16C2×C43⋊#95C2212yes—
17#14582634—24no—
18C22×C42×C43C2211yescharacteristic
19C2×C22⋊C8×C43C2212yes—
20C43×#336—22no—
21C22×D172C2×C411yescharacteristic
22C22×C22⋊D43—21no—
23C23×Dic43—22no—
24#13063308—44no—
25#13063299—22no—
26#13063299—22no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C412yes—
29C2×Dic43⋊C4—22no—
30C2×C22⋊Dic43—21no—
31C2×(C2×D43)⋊C4—22no—
32C2×(C2×D43)⋊C4—22no—
33C2×(C2×D43)⋊C4—21no—
34C43⋊#95—24no—
35C43⋊#95—24no—
36C43⋊#95—22no—
37C43⋊#95—21no—
38C43⋊#95—22no—
39C43⋊#95D414yes—
40C23×C4×C43D411yescharacteristic
41C23×C4×C43D411yescharacteristic
42C23×C4×C43C2311yescharacteristic
43C22×C8×C43—22no—
44C2×C42×C43—22no—
45C2×C42×C43—22no—
46C2×C42×C43C2×C412yes—
47C2×C42×C43D412yes—
48C22⋊C8×C43—22no—
49C22⋊C8×C43—22no—
50C24×C43C2×D411yescharacteristic
51C23×D43—21no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—42no—
59C22×C4×C43—42no—
60C22×C4×C43C22⋊C412yes—
61C22×C4×C43C22⋊C412yes—
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D412yes—
65C22×C4×C43#4112yes—
66C2×C22⋊D43—41no—
67C2×C22⋊D43—41no—
68C2×C22⋊D43—42no—
69C2×C22⋊D43—42no—
70C22×Dic43—22no—
71C22×Dic43—21no—
72C22×Dic43—24no—
73C22×Dic43—44no—
74C22×Dic43—44no—
75C22×Dic43—42no—
76C22×Dic43—42no—
77C2×D172—22no—
78C2×D172—42no—
79C2×C8×C43—44no—
80C2×C8×C43—42no—
81C42×C43—24no—
82C42×C43—24no—
83C22⋊Dic43—42no—
84(C2×D43)⋊C4—44no—
85(C2×D43)⋊C4—44no—
86(C2×D43)⋊C4—42no—
87C4⋊Dic43—22no—
88C4⋊Dic43—42no—
89Dic43⋊C4—44no—
90C23×C43—22no—
91C23×C43—22no—
92C23×C43C2×C22⋊C411yescharacteristic
93C23×C43#12011yescharacteristic
94C23×C43#12311yescharacteristic
95C23×C43#13512yes—
96C23×C43AGL(1,ℤ/8)12yes—
97C22×D43—41no—
98C22×D43—42no—
99C22×D43—41no—
100C22×D43—41no—
101C22×D43—42no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—22no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—42no—
115C2×C4×C43—42no—
116C2×C4×C43C4×D412yes—
117C2×C4×C43#12112yes—
118C22⋊D43—82no—
119C22⋊D43—82no—
120C2×Dic43—44no—
121C2×Dic43—44no—
122C2×Dic43—41no—
123C2×Dic43—42no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—42no—
127C2×Dic43—42no—
128C2×Dic43—44no—
129C2×Dic43—84no—
130C2×Dic43—84no—
131D172—82no—
132C8×C43—82no—
133#9157—431nomaximal, Sylow
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—21no—
138C22×C43—24no—
139C22×C43—24no—
140C22×C43#38611yescharacteristic
141C22×C43#41012yes—
142C22×C43#41611yescharacteristic
143C22×C43#41811yescharacteristic
144C22×C43#42112yes—
145C22×C43#44912yes—
146C22×C43#48212yes—
147C2×D43—81no—
148C2×D43—81no—
149C2×D43—81no—
150C2×D43—82no—
151C2×D43—82no—
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—42no—
155C4×C43—42no—
156Dic43—84no—
157Dic43—81no—
158Dic43—82no—
159#2854—431no—
160C2×#383—431no—
161#1817D4311yescharacteristic, complemented
162C2×#327—432no—
163#1294—432no—
164C2×C43—22no—
165C2×C43—22no—
166C2×C43#151412yes—
167C2×C43#152112yes—
168C2×C43#187511yescharacteristic
169C2×C43#189711yescharacteristic
170C2×C43#189911yescharacteristic
171D43—161no—
172C2×#123—861no—
173C2×#121—431no—
174C22×C42C2×D4311yescharacteristic
175C2×C22⋊C8C2×D4312yes—
176#390—432no—
177#389—432no—
178#388—862no—
179#386—861no—
180#383—864no—
181#380—431no—
182C2×#95—432no—
183C2×#95—861no—
184C2×#95—861no—
185#336—22no—
186#327—864no—
187C43#915711yescharacteristic, complemented, Sylow
188C22×D4—431no—
189C22×D4—861no—
190C23×C4—862no—
191C23×C4D17211yescharacteristic
192C23×C4D17211yescharacteristic
193C23×C4C22×D4311yescharacteristic
194C22×C8—22no—
195#123—1724no—
196#121—862no—
197#121—862no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4—432no—
200C2×C4⋊C4—862no—
201C2×C22⋊C4—861no—
202C2×C22⋊C4—862no—
203C2×C22⋊C4—862no—
204C2×C22⋊C4—861no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42C4×D4312yes—
208C2×C42C22⋊D4312yes—
209C22⋊C8—22no—
210C22⋊C8—22no—
211#95—434no—
212#95—864no—
213#95—864no—
214#95—862no—
215#95—862no—
216#95—861no—
217C24—861no—
218C24C2×D17211yescharacteristic
219C2×D4—862no—
220C2×D4—1722no—
221C2×D4—1721no—
222C2×D4—1721no—
223C2×D4—1722no—
224C2×D4—1722no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—862no—
234C22×C4—861no—
235C22×C4—864no—
236C22×C4—1724no—
237C22×C4—1724no—
238C22×C4—1722no—
239C22×C4—1722no—
240C22×C4(C2×D43)⋊C412yes—
241C22×C4(C2×D43)⋊C412yes—
242C22×C4C2×C4×D4311yescharacteristic
243C22×C4D4×D4312yes—
244C22×C4#1062190012yes—
245C22×C4C2×C22⋊D4311yescharacteristic
246C2×C8—44no—
247C2×C8—42no—
248C4⋊C4—862no—
249C4⋊C4—1722no—
250C4⋊C4—1724no—
251C22⋊C4—1724no—
252C22⋊C4—1724no—
253C22⋊C4—1722no—
254C22⋊C4—1722no—
255C42—24no—
256C42—24no—
257C23—22no—
258C23—22no—
259C23—1722no—
260C23—1721no—
261C23—1721no—
262C23—1722no—
263C23—1721no—
264C23C2×(C2×D43)⋊C411yescharacteristic
265C23#1306329511yescharacteristic
266C23#1306330911yescharacteristic
267C23#1306334712yes—
268C23#1306335312yes—
269D4—3442no—
270D4—3442no—
271D4—3442no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—3444no—
287C2×C4—3444no—
288C2×C4—1724no—
289C2×C4—1724no—
290C2×C4—1724no—
291C2×C4—1722no—
292C2×C4—1721no—
293C2×C4—1722no—
294C2×C4—1721no—
295C2×C4—1722no—
296C2×C4—1721no—
297C2×C4(C22⋊D43)⋊C412yes—
298C2×C4#1306329712yes—
299C8—82no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—24no—
305C22—24no—
306C22—3441no—
307C22—3441no—
308C22—3441no—
309C22—3442no—
310C22—3442no—
311C22#1458277611yescharacteristic
312C22#1458287212yes—
313C22#1458289611yescharacteristic
314C22#1458290511yescharacteristic
315C22#1458291512yes—
316C22#1458304612yes—
317C22#1458322412yes—
318C4—22no—
319C4—22no—
320C4—42no—
321C4—42no—
322C4—3444no—
323C4—3441no—
324C4—3442no—
325C2—22no—
326C2—22no—
327C2—6881no—
328C2#1913314312yes—
329C2#1913317312yes—
330C2#1913491511yescharacteristic
331C2#1913504111yescharacteristic
332C2#1913505111yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1817C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1817D43
hypocenterC43#9157
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#14582767C2semidirect
4. #19132475C2semidirect
5. C43×#1817C2semidirect
8. #14582801C4semidirect
9. #14582797C4semidirect
161. #1817D43semidirect
187. C43#9157semidirect

Maximal subgroups

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

subgroupindex
#191429262
C2×#145827672
C2×#145826342
#191324752
C43×#18172
#915743