Finite Group Databasebeta

← #24992355

Subgroups — #24992355

Order 11008.

630 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 143 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#19142934C211yesmaximal, characteristic
2C2×#14582765C211yesmaximal, characteristic
3C2×#14582637C212yesmaximal
4#19132475C212yesmaximal
5C43×#1817C211yesmaximal, characteristic
6C2×#13063304C2211yescharacteristic
7C22×C4⋊Dic43—21no—
8#14582805C412yescomplemented
9#14582797C412yescomplemented
10#14582783—22no—
11#14582772—21no—
12#14582765—24no—
13#14582762—21no—
14#14582759C2211yescharacteristic
15C2×C43⋊#95—21no—
16C2×C43⋊#95C2212yes—
17#14582637—24no—
18C22×C42×C43C2211yescharacteristic
19C2×C22⋊C8×C43C2212yes—
20C43×#336—22no—
21C22×Dic86C2×C411yescharacteristic
22C23×Dic43—22no—
23#13063304—22no—
24#13063304—22no—
25C2×C4⋊Dic43—24no—
26C2×C4⋊Dic43—42no—
27C2×C4⋊Dic43—42no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C4⋊Dic43C2×C412yes—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C43⋊#95—24no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—21no—
40C43⋊#95D414yes—
41C23×C4×C43D411yescharacteristic
42C23×C4×C43D411yescharacteristic
43C23×C4×C43C2311yescharacteristic
44C22×C8×C43—22no—
45C2×C42×C43—22no—
46C2×C42×C43—22no—
47C2×C42×C43C2×C412yes—
48C2×C42×C43D412yes—
49C22⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51C24×C43C2×D411yescharacteristic
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—42no—
59C22×C4×C43—42no—
60C22×C4×C43C22⋊C412yes—
61C22×C4×C43C22⋊C412yes—
62C22×C4×C43SD1612yes—
63C22×C4×C43Q1612yes—
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D412yes—
67C22×C4×C43#4112yes—
68C22×Dic43—22no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—24no—
72C22×Dic43—44no—
73C22×Dic43—44no—
74C22×Dic43—42no—
75C22×Dic43—42no—
76C2×Dic86—22no—
77C2×Dic86—42no—
78C2×C8×C43—44no—
79C2×C8×C43—42no—
80C42×C43—24no—
81C42×C43—24no—
82C22⋊Dic43—41no—
83C22⋊Dic43—41no—
84C22⋊Dic43—41no—
85C22⋊Dic43—41no—
86C4⋊Dic43—22no—
87C4⋊Dic43—48no—
88C4⋊Dic43—42no—
89Dic43⋊C4—44no—
90Dic43⋊C4—42no—
91C23×C43—22no—
92C23×C43—22no—
93C23×C43C2×C22⋊C411yescharacteristic
94C23×C43#12011yescharacteristic
95C23×C43#12311yescharacteristic
96C23×C43C2×SD1611yescharacteristic
97C23×C43C2×Q1611yescharacteristic
98C23×C43AGL(1,ℤ/8)11yescharacteristic
99C23×C43#13711yescharacteristic
100C2×C4×C43—22no—
101C2×C4×C43—22no—
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—22no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—42no—
115C2×C4×C43#10314yes—
116C2×C4×C43C4×D412yes—
117C2×C4×C43#12112yes—
118C2×Dic43—44no—
119C2×Dic43—44no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—42no—
123C2×Dic43—42no—
124C2×Dic43—42no—
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—44no—
128C2×Dic43—84no—
129C2×Dic43—84no—
130Dic86—82no—
131C8×C43—82no—
132#9152—431nomaximal, Sylow
133C22×C43—21no—
134C22×C43—21no—
135C22×C43—21no—
136C22×C43—21no—
137C22×C43—22no—
138C22×C43—22no—
139C22×C43—22no—
140C22×C43—22no—
141C22×C43#38611yescharacteristic
142C22×C43#41012yes—
143C22×C43C2×#10311yescharacteristic
144C22×C43#41711yescharacteristic
145C22×C43#42112yes—
146C22×C43#45011yescharacteristic
147C22×C43#45111yescharacteristic
148C22×C43#48311yescharacteristic
149C22×C43#48411yescharacteristic
150C4×C43—24no—
151C4×C43—22no—
152C4×C43—22no—
153C4×C43—42no—
154Dic43—84no—
155Dic43—81no—
156Dic43—81no—
157Dic43—82no—
158#2855—431no—
159C2×#382—431no—
160#1817D4311yescharacteristic
161C2×#328—432no—
162#1294—432no—
163C2×C43—21no—
164C2×C43—21no—
165C2×C43—21no—
166C2×C43—21no—
167C2×C43#151212yes—
168C2×C43#151812yes—
169C2×C43#187211yescharacteristic
170C2×C43#189711yescharacteristic
171C2×C43#189911yescharacteristic
172C2×C22⋊Q8—431no—
173C22×C4⋊C4—861no—
174C22×C42C2×D4311yescharacteristic
175C2×C22⋊C8C2×D4312yes—
176#391—432no—
177#389—432no—
178#387—862no—
179#385—861no—
180#382—864no—
181#381—861no—
182#380—431no—
183C2×#95—432no—
184C2×#95—861no—
185#336—22no—
186#328—864no—
187C43#915211yescharacteristic, complemented, Sylow
188C22×Q8—431no—
189C23×C4—862no—
190C23×C4D17211yescharacteristic
191C23×C4D17211yescharacteristic
192C23×C4C22×D4311yescharacteristic
193C22×C8—22no—
194C22⋊Q8—862no—
195C22⋊Q8—862no—
196C2×C4⋊C4—431no—
197C2×C4⋊C4—432no—
198C2×C4⋊C4—864no—
199C2×C4⋊C4—862no—
200C2×C4⋊C4—861no—
201C2×C4⋊C4—1722no—
202C2×C4⋊C4—1722no—
203C2×C22⋊C4—861no—
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—862no—
214#95—862no—
215#95—862no—
216#95—862no—
217#95—861no—
218C24C2×D17211yescharacteristic
219C2×Q8—862no—
220C2×Q8—1722no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—862no—
230C22×C4—861no—
231C22×C4—861no—
232C22×C4—864no—
233C22×C4—1724no—
234C22×C4—1724no—
235C22×C4—1722no—
236C22×C4—1722no—
237C22×C4#1062187312yes—
238C22×C4Dic17212yes—
239C22×C4(C2×D43)⋊C412yes—
240C22×C4(C2×D43)⋊C412yes—
241C22×C4C2×C4×D4311yescharacteristic
242C22×C4D4×D4312yes—
243C22×C4#1062190012yes—
244C22×C4C2×C22⋊D4311yescharacteristic
245C2×C8—44no—
246C2×C8—42no—
247C4⋊C4—862no—
248C4⋊C4—1722no—
249C4⋊C4—1728no—
250C4⋊C4—1724no—
251C4⋊C4—1722no—
252C22⋊C4—1721no—
253C22⋊C4—1721no—
254C22⋊C4—1721no—
255C22⋊C4—1721no—
256C42—24no—
257C42—24no—
258C23—22no—
259C23—22no—
260C23C2×(C2×D43)⋊C411yescharacteristic
261C23#1306329511yescharacteristic
262C23#1306330911yescharacteristic
263C23C2×#1062187311yescharacteristic
264C23C2×Dic17211yescharacteristic
265C23#1306335311yescharacteristic
266C23#1306335811yescharacteristic
267Q8—3442no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—3444no—
284C2×C4—3444no—
285C2×C4—1724no—
286C2×C4—1724no—
287C2×C4—1724no—
288C2×C4—1722no—
289C2×C4—1722no—
290C2×C4—1722no—
291C2×C4—1722no—
292C2×C4—1722no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4#1306325014yes—
296C2×C4(C22⋊D43)⋊C412yes—
297C2×C4#1306329712yes—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22#1458277611yescharacteristic
308C22#1458287212yes—
309C22C2×#1306325011yescharacteristic
310C22#1458290111yescharacteristic
311C22#1458291512yes—
312C22#1458305211yescharacteristic
313C22#1458305711yescharacteristic
314C22#1458323011yescharacteristic
315C22#1458323511yescharacteristic
316C4—22no—
317C4—22no—
318C4—24no—
319C4—42no—
320C4—3444no—
321C4—3441no—
322C4—3441no—
323C4—3442no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2#1913313412yes—
329C2#1913316012yes—
330C2#1913490011yescharacteristic
331C2#1913504111yescharacteristic
332C2#1913505111yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1817C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1817D43
hypocenterC43#9152
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
8. #14582805C4semidirect
9. #14582797C4semidirect
187. C43#9152semidirect

Maximal subgroups

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

subgroupindex
#191429342
C2×#145827652
C2×#145826372
#191324752
C43×#18172
#915243