Finite Group Databasebeta

← #24989490

Subgroups — #24989490

Order 11008.

550 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic
2#19134618C212yesmaximal, complemented
3#19134580C212yesmaximal
4#19132463C211yesmaximal, characteristic, complemented
5C43×#1289C211yesmaximal, characteristic, complemented
6C23×C43⋊C8C2211yescharacteristic
7C22×C8×D43C411yescharacteristic, complemented
8C2×C4×C22⋊D43C2211yescharacteristic
9(C22⋊D43)⋊C8—22no—
10(C22⋊D43)⋊C8—22no—
11C2×#13063256—22no—
12C2×Dic43⋊C8C411yescharacteristic, complemented
13C2×#13063239—22no—
14C2×(C2×D43)⋊C8C411yescharacteristic, complemented
15C2×C8×Dic43C411yescharacteristic, complemented
16#14582759C2212yes—
17#14582665—22no—
18#14582661—22no—
19C2×C22⋊C8×C43C2211yescharacteristic
20C43×#380C2212yes—
21C22×C22⋊D43D411yescharacteristic
22C22×C4×D43C2×C411yescharacteristic
23C22×C43⋊C8—42no—
24C22×C43⋊C8C2×C411yescharacteristic
25C22×C43⋊C8C2×C411yescharacteristic
26C22×C43⋊C8D412yes—
27C22×C43⋊C8D412yes—
28C2×C8×D43—21no—
29C2×C8×D43—21no—
30C2×C8×D43—42no—
31C4×C22⋊D43—22no—
32C4×C22⋊D43—22no—
33C2×C4⋊Dic43—22no—
34C2×Dic43⋊C4Q811yescharacteristic
35C2×C22⋊Dic43—22no—
36C2×C22⋊Dic43D411yescharacteristic
37C2×(C2×D43)⋊C4Q811yescharacteristic
38C2×C4×Dic43C2×C411yescharacteristic
39#13063256—44no—
40Dic43⋊C8—22no—
41#13063239—44no—
42(C2×D43)⋊C8—22no—
43C8×Dic43—21no—
44C8×Dic43—21no—
45C43⋊#95—22no—
46C23×C4×C43C2311yescharacteristic
47C22×C8×C43C2×C411yescharacteristic
48C22×C8×C43C2×C411yescharacteristic
49C2×C4⋊C4×C43—22no—
50C2×C22⋊C4×C43—22no—
51C22⋊C8×C43—22no—
52#95×C43—22no—
53C24×C43C2×D411yescharacteristic
54C23×D43C4⋊C411yescharacteristic
55C22×C4×C43—41no—
56C22×C4×C43—41no—
57C22×C4×C43—42no—
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D412yes—
60C22×C4×C43C2×Q811yescharacteristic
61C22×C4×C43#4112yes—
62C2×C22⋊D43—22no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43SD1614yes—
66C22×Dic43—42no—
67C22×Dic43C4⋊C411yescharacteristic
68C22×Dic43C4⋊C411yescharacteristic
69C22×Dic43C4⋊C411yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43—41no—
73C2×C4×D43—41no—
74C2×C8×C43—21no—
75C2×C8×C43—21no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C4⋊C4×C43—42no—
79C4⋊C4×C43—42no—
80C22⋊C4×C43—42no—
81C22⋊C4×C43—42no—
82C22⋊Dic43—22no—
83C22⋊Dic43—42no—
84C22⋊Dic43—42no—
85(C2×D43)⋊C4—22no—
86C4⋊Dic43—42no—
87C4⋊Dic43—42no—
88Dic43⋊C4—22no—
89C4×Dic43—21no—
90C4×Dic43—21no—
91C2×C43⋊C8—24no—
92C2×C43⋊C8—22no—
93C2×C43⋊C8—41no—
94C2×C43⋊C8—42no—
95C2×C43⋊C8C22⋊C411yescharacteristic
96C2×C43⋊C8C22⋊C412yes—
97C2×C43⋊C8C22⋊C411yescharacteristic
98C8×D43—42no—
99C8×D43—42no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43C2×C4⋊C411yescharacteristic
103C23×C43#12112yes—
104C23×C43C2×SD1612yes—
105C23×C43#13511yescharacteristic
106C23×C43#13511yescharacteristic
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—41no—
110C22×D43—41no—
111C22×D43#10612yescomplemented
112C2×C4×C43—22no—
113C2×C4×C43—21no—
114C2×C4×C43—22no—
115C2×C4×C43—21no—
116C2×C4×C43—41no—
117C2×C4×C43—42no—
118C2×C4×C43—82no—
119C2×C4×C43—82no—
120C2×C4×C43—82no—
121C2×C4×C43C2×C22⋊C411yescharacteristic
122C2×C4×C43#11711yescharacteristic
123C2×C4×C43C22⋊Q812yes—
124C22⋊D43—24no—
125C22⋊D43—24no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—82no—
133C2×Dic43—82no—
134C2×Dic43—82no—
135C2×Dic43#10612yescomplemented
136C4×D43—42no—
137C4×D43—41no—
138C4×D43—41no—
139C8×C43—41no—
140C8×C43—41no—
141C43⋊C8—21no—
142C43⋊C8—22no—
143C43⋊C8#9912yescomplemented
144#8608—431nomaximal, Sylow
145C22×C43—21no—
146C22×C43—22no—
147C22×C43—21no—
148C22×C43—22no—
149C22×C43—42no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43#38011yescharacteristic
153C22×C43C2×#10611yescharacteristic
154C22×C43#42711yescharacteristic
155C22×C43#46512yes—
156C22×C43#46512yes—
157C2×D43—22no—
158C2×D43—42no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—42no—
162C4×C43—21no—
163C4×C43—22no—
164C4×C43—162no—
165C4×C43C2×#9911yescharacteristic
166C4×C43#41011yescharacteristic
167Dic43—22no—
168Dic43—41no—
169Dic43—41no—
170Dic43—162no—
171C2×C8×D4—431no—
172#1807—432no—
173#1799—432no—
174#1289—431no—
175#1289D4311yescharacteristic, complemented
176C2×C43—22no—
177C2×C43—22no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43#179911yescharacteristic
181C2×C43#180711yescharacteristic
182C2×C43#181211yescharacteristic
183D43—42no—
184C23×C8—431no—
185C23×C8—431no—
186C2×C4×D4—431no—
187C8×D4—862no—
188C8×D4—862no—
189C2×#106—862no—
190C2×C4⋊C8—431no—
191C2×#99—862no—
192C2×C22⋊C8—431no—
193C2×C22⋊C8C2×D4311yescharacteristic
194C2×C4×C8—431no—
195#380—432no—
196#380C2×D4312yes—
197#342—862no—
198#340—862no—
199C43#860811yescharacteristic, complemented, Sylow
200C22×D4—431no—
201C23×C4—431no—
202C23×C4C22×D4311yescharacteristic
203C22×C8—431no—
204C22×C8—432no—
205C22×C8—431no—
206C22×C8—432no—
207C22×C8—861no—
208C22×C8—861no—
209C22×C8—1722no—
210C22×C8—1722no—
211C22×C8C4×D4311yescharacteristic
212C22×C8C4×D4311yescharacteristic
213C4×D4—862no—
214C4×D4—862no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—431no—
217C2×C4⋊C4—862no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—431no—
220C2×C22⋊C4—431no—
221C2×C22⋊C4—862no—
222C2×C42—431no—
223#106—1724no—
224C4⋊C8—862no—
225#99—1724no—
226C22⋊C8—22no—
227C22⋊C8—862no—
228C4×C8—861no—
229C4×C8—861no—
230#95—22no—
231#95—862no—
232C24—431no—
233C24D4×D4311yescharacteristic
234C2×D4—434no—
235C2×D4—862no—
236C2×D4—861no—
237C2×D4—861no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—42no—
241C22×C4—431no—
242C22×C4—431no—
243C22×C4—431no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—1721no—
247C22×C4—1721no—
248C22×C4—1722no—
249C22×C4C2×C4×D4311yescharacteristic
250C22×C4#1062189812yes—
251C22×C4D4×D4312yes—
252C22×C4Q8×D4311yescharacteristic
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—431no—
258C2×C8—431no—
259C2×C8—432no—
260C2×C8—864no—
261C2×C8—862no—
262C2×C8—1722no—
263C2×C8—1722no—
264C2×C8—1722no—
265C2×C8—1721no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—862no—
269C4⋊C4—1722no—
270C4⋊C4—1722no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—862no—
274C22⋊C4—862no—
275C22⋊C4—1722no—
276C22⋊C4—1722no—
277C42—861no—
278C42—861no—
279C23—41no—
280C23—41no—
281C23—432no—
282C23—861no—
283C23—861no—
284C23—1721no—
285C23—1721no—
286C23C4⋊C4×D4311yescharacteristic
287C23#1306329812yes—
288C23SD16×D4312yes—
289C23#1306334411yescharacteristic
290C23#1306334811yescharacteristic
291D4—864no—
292D4—864no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—432no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—3442no—
308C2×C4—3442no—
309C2×C4—3442no—
310C2×C4—1722no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4C22⋊C4×D4311yescharacteristic
316C2×C4#1306328211yescharacteristic
317C2×C4#1306330312yes—
318C8—41no—
319C8—41no—
320C8—432no—
321C8—861no—
322C8—862no—
323C22—22no—
324C22—21no—
325C22—22no—
326C22—21no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22—862no—
331C22—1722no—
332C22—1722no—
333C22—1721no—
334C22—1721no—
335C22#1458275811yescharacteristic
336C22#106×D4311yescharacteristic
337C22#1458293611yescharacteristic
338C22#1458312712yes—
339C22#1458313112yes—
340C4—21no—
341C4—22no—
342C4—162no—
343C4—862no—
344C4—1721no—
345C4—1721no—
346C4—6882no—
347C4#99×D4311yescharacteristic
348C4#1458287111yescharacteristic
349C2—22no—
350C2—22no—
351C2—21no—
352C2—21no—
353C2—1722no—
354C2#1913458211yescharacteristic
355C2#1913461911yescharacteristic
356C2#1913464011yescharacteristic
subgroupG/H
centerC22#14582758
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1289C2
socleC22×C43#380
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1289D43
hypocenterC43#8608
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #19134618C2semidirect
4. #19132463C2semidirect
5. C43×#1289C2semidirect
7. C22×C8×D43C4semidirect
12. C2×Dic43⋊C8C4semidirect
14. C2×(C2×D43)⋊C8C4semidirect
15. C2×C8×Dic43C4semidirect
111. C22×D43#106semidirect
135. C2×Dic43#106semidirect
143. C43⋊C8#99semidirect
175. #1289D43semidirect
199. C43#8608semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D43)⋊C82
#191346182
#191345802
#191324632
C43×#12892
#860843