Finite Group Databasebeta

← #25066002

Subgroups — #25066002

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#10621902C212yesmaximal, complemented
2C4×#13063348C211yesmaximal, characteristic
3#19133420C211yesmaximal, characteristic, complemented
4#19133418C211yesmaximal, characteristic, complemented
5#19133414C211yesmaximal, characteristic, complemented
6#19133410C212yesmaximal, complemented
7#19133405C212yesmaximal, complemented
8#19133340C211yesmaximal, characteristic, complemented
9#19132976C212yesmaximal, complemented
10#322×D43C211yesmaximal, characteristic, complemented
11C43×#1579C211yesmaximal, characteristic, complemented
12C2×#13063348C411yescharacteristic
13C4×#10621902C2212yes—
14Q8×C43⋊C8C2212yes—
15Q16×Dic43C411yescharacteristic
16C4×#10621884C2212yes—
17#14582984C412yes—
18C4×D344C2211yescharacteristic
19#14582981C411yescharacteristic
20C8×D172—22no—
21C8×D172C2212yes—
22#14582964—22no—
23#14582964C2212yes—
24#14582951—22no—
25#14582951C2212yes—
26#14582936C411yescharacteristic
27#14582894C412yes—
28C4×C8×D43—22no—
29C4×C8×D43C2211yescharacteristic
30C4×C8×D43C2211yescharacteristic
31C4×C8×D43C2211yescharacteristic
32#14582651C2212yes—
33#14582650C2211yescharacteristic
34Q8⋊(C43⋊C8)C2212yes—
35#14582628C2212yes—
36#14582626C2212yes—
37#14582621C2211yescharacteristic
38#14582621C2211yescharacteristic
39#14582620C2211yescharacteristic
40C8×Q8×C43C2212yes—
41C4×Q16×C43C2211yescharacteristic
42C43×#334C2211yescharacteristic
43C43×Q8⋊C8C2212yes—
44C43×#322C2211yescharacteristic
45C2×#10621902C2×C412yes—
46#13063348C818yescomplemented
47C2×#10621884C2×C412yes—
48C2×D344C2×C411yescharacteristic
49C2×C8×D43—21no—
50C2×C8×D43—22no—
51C2×C8×D43—22no—
52C2×C8×D43C2×C411yescharacteristic
53C2×C8×D43C2×C411yescharacteristic
54C2×C8×D43D412yes—
55Q8×Dic43C2×C412yes—
56C4×D172—22no—
57C4×D172C2312yes—
58#13063287—22no—
59#13063287C2×C412yes—
60#13063283—22no—
61#13063283C2×C412yes—
62C42×D43—22no—
63C42×D43C2311yescharacteristic
64#13063259C2×C411yescharacteristic
65#13063256C2×C412yes—
66C4⋊(C43⋊C8)—22no—
67C4⋊(C43⋊C8)C2312yes—
68#13063249C2×C412yes—
69#13063247C2×C412yes—
70#13063245C2×C412yes—
71(C2×D43)⋊C8—22no—
72(C2×D43)⋊C8—22no—
73(C2×D43)⋊C8—22no—
74C4×C43⋊C8—22no—
75C4×C43⋊C8C2311yescharacteristic
76C4×C43⋊C8C2311yescharacteristic
77C4×C43⋊C8C2311yescharacteristic
78C8×Dic43—22no—
79C8×Dic43—21no—
80C8×Dic43C2×C411yescharacteristic
81C8×Dic43C2×C411yescharacteristic
82C8×Dic43D412yes—
83C2×Q16×C43C2×C411yescharacteristic
84C4×Q8×C43C2312yes—
85#107×C43C2×C411yescharacteristic
86C4⋊C8×C43—22no—
87C4⋊C8×C43C2312yes—
88#103×C43C2×C412yes—
89C4×C8×C43—22no—
90C4×C8×C43C2311yescharacteristic
91C4×C8×C43C2311yescharacteristic
92C4×C8×C43C2311yescharacteristic
93C2×Q8×C43C22×C412yes—
94#10621902—24no—
95#10621902C2×C818yescomplemented
96C2×D172—22no—
97C2×D172C22×C412yes—
98C2×C4×D43—22no—
99C2×C4×D43—22no—
100C2×C4×D43—22no—
101C2×C4×D43C22×C411yescharacteristic
102C2×C4×D43C2×D411yescharacteristic
103C2×C4×D43#4111yescharacteristic
104Q16×C43C2×C814yescomplemented
105C2×C8×C43—22no—
106C2×C8×C43—21no—
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C22×C411yescharacteristic
109C2×C8×C43C2×D412yes—
110C4⋊C4×C43—22no—
111C4⋊C4×C43C22×C412yes—
112C42×C43—22no—
113C42×C43C2411yescharacteristic
114#10621884C2×C818yescomplemented
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—22no—
117(C2×D43)⋊C4—22no—
118C4⋊Dic43—22no—
119C4⋊Dic43C22×C412yes—
120C4×Dic43—22no—
121C4×Dic43—22no—
122C4×Dic43C22×C411yescharacteristic
123C4×Dic43C2×D411yescharacteristic
124C4×Dic43#4111yescharacteristic
125C2×C43⋊C8—22no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8C22×C411yescharacteristic
128C2×C43⋊C8C22×C411yescharacteristic
129C2×C43⋊C8C2×D412yes—
130D344C2×C814yescomplemented
131C8×D43—22no—
132C8×D43—42no—
133C8×D43—44no—
134C8×D43—44no—
135C8×D43—42no—
136C8×D43C2×C814yescomplemented
137C22×D43—22no—
138C22×D43C4×D411yescharacteristic
139Q8×C43—22no—
140Q8×C43C22×C814yes—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43C23×C411yescharacteristic
144C2×C4×C43C22×D411yescharacteristic
145C2×C4×C43C2×#4111yescharacteristic
146C2×Dic43—22no—
147C2×Dic43C4×D411yescharacteristic
148C2×Dic43C4×D411yescharacteristic
149C2×Dic43C4×D411yescharacteristic
150D172—28no—
151D172—22no—
152D172C22×C814yes—
153C4×D43—22no—
154C4×D43—28no—
155C4×D43—22no—
156C4×D43—42no—
157C4×D43—42no—
158C4×D43—44no—
159C4×D43C22×C812yes—
160C4×D43#13112yes—
161C8×C43—21no—
162C8×C43—22no—
163C8×C43—41no—
164C8×C43—42no—
165C8×C43C22×C812yes—
166C43⋊C8—21no—
167C43⋊C8—22no—
168C43⋊C8—41no—
169C43⋊C8—42no—
170C43⋊C8C22×C812yes—
171#17849—431nomaximal, Sylow
172C22×C43C2×C4×D411yescharacteristic
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—24no—
176C2×D43—42no—
177C2×D43—42no—
178C2×D43C8×D412yes—
179C4×C43—24no—
180C4×C43—21no—
181C4×C43—42no—
182C4×C43C23×C811yescharacteristic
183C4×C43C2×#13111yescharacteristic
184C4×C43#57512yes—
185Dic43—21no—
186Dic43—42no—
187Dic43C8×D412yes—
188Dic43#44412yes—
189C8×#41—432no—
190C4×#135—431no—
191#1580—431no—
192#1580—431no—
193#1579—431no—
194#1579D4311yescharacteristic, complemented
195SD16⋊C8—432no—
196SD16⋊C8—432no—
197#1564—431no—
198#1476—432no—
199C2×#322—431no—
200C2×C43C2×C8×D411yescharacteristic
201C2×C43#294311yescharacteristic
202C2×C43C2×#44411yescharacteristic
203D43—22no—
204D43—44no—
205C2×#135—431no—
206C4×#41—432no—
207C8×Q8—432no—
208C8×Q8C2×D4312yes—
209C4×Q16—431no—
210C4×Q16C2×D4311yescharacteristic
211C4×SD16—432no—
212C4×SD16—432no—
213C4×D8—431no—
214C4×D8—431no—
215C8×D4—432no—
216C8×D4—432no—
217C8×D4—862no—
218C8×D4—862no—
219#431—432no—
220#431—862no—
221#427—431no—
222#416—432no—
223C2×C4×C8—431no—
224C2×C4×C8—431no—
225C2×C4×C8—431no—
226C2×C4×C8—862no—
227#335—432no—
228#334—431no—
229#334C2×D4311yescharacteristic
230Q8⋊C8—432no—
231Q8⋊C8C2×D4312yes—
232D4⋊C8—432no—
233D4⋊C8—432no—
234#322—431no—
235#322—431no—
236#322—431no—
237#322C2×D4311yescharacteristic
238C43#1784911yescharacteristic, complemented, Sylow
239C2×#41—432no—
240#135—438no—
241C2×Q16C4×D4311yescharacteristic
242C2×SD16—432no—
243C2×D8—431no—
244C22×C8—431no—
245C22×C8—431no—
246C22×C8—432no—
247C22×C8—862no—
248C22×C8—861no—
249C22×C8—862no—
250C4×Q8—432no—
251C4×Q8C22×D4312yes—
252C4×D4—432no—
253C4×D4—432no—
254C4×D4—862no—
255C4×D4—862no—
256#117—432no—
257#117—862no—
258C2×C42—431no—
259C2×C42—862no—
260#107—431no—
261#107C4×D4311yescharacteristic
262#106—432no—
263C4⋊C8—22no—
264C4⋊C8—432no—
265C4⋊C8—862no—
266C4⋊C8C22×D4312yes—
267#103—432no—
268#103C4×D4312yes—
269#102—432no—
270#102—432no—
271C22⋊C8—862no—
272C22⋊C8—862no—
273C22⋊C8—862no—
274C4×C8—22no—
275C4×C8—431no—
276C4×C8—431no—
277C4×C8—432no—
278C4×C8—431no—
279C4×C8—431no—
280C4×C8—431no—
281C4×C8—862no—
282C4×C8—861no—
283C4×C8—862no—
284C4×C8C22×D4311yescharacteristic
285C4×C8C22×D4311yescharacteristic
286C4×C8C22×D4311yescharacteristic
287#41—438no—
288#41—864no—
289C2×Q8C2×C4×D4312yes—
290C2×D4—432no—
291C2×D4—862no—
292C22×C4—431no—
293C22×C4—431no—
294C22×C4—431no—
295C22×C4—862no—
296C22×C4—862no—
297C22×C4—862no—
298Q16C8×D4314yescomplemented
299SD16—438no—
300D8—434no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—431no—
304C2×C8—434no—
305C2×C8—431no—
306C2×C8—432no—
307C2×C8—862no—
308C2×C8—862no—
309C2×C8—861no—
310C2×C8—1722no—
311C2×C8—1724no—
312C2×C8—1724no—
313C2×C8—1722no—
314C2×C8C2×C4×D4311yescharacteristic
315C2×C8C2×C4×D4311yescharacteristic
316C2×C8D4×D4312yes—
317C4⋊C4—22no—
318C4⋊C4—432no—
319C4⋊C4—862no—
320C4⋊C4C2×C4×D4312yes—
321C22⋊C4—862no—
322C22⋊C4—862no—
323C22⋊C4—862no—
324C42—22no—
325C42—431no—
326C42—431no—
327C42—431no—
328C42—862no—
329C42—862no—
330C42C23×D4311yescharacteristic
331C23—431no—
332C23—862no—
333Q8—22no—
334Q8C2×C8×D4314yes—
335D4—434no—
336D4—868no—
337D4—862no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—431no—
341C2×C4—431no—
342C2×C4—432no—
343C2×C4—432no—
344C2×C4—431no—
345C2×C4—862no—
346C2×C4—868no—
347C2×C4—862no—
348C2×C4—862no—
349C2×C4—1724no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4C22×C4×D4311yescharacteristic
353C2×C4C2×D4×D4311yescharacteristic
354C2×C4#41×D4311yescharacteristic
355C8—21no—
356C8—22no—
357C8—41no—
358C8—42no—
359C8—432no—
360C8—861no—
361C8—862no—
362C8—1721no—
363C8—1722no—
364C8C2×C8×D4312yes—
365C22—432no—
366C22—861no—
367C22—861no—
368C22—864no—
369C22—1722no—
370C22—1722no—
371C22C4×D4×D4311yescharacteristic
372C4—21no—
373C4—24no—
374C4—42no—
375C4—432no—
376C4—432no—
377C4—861no—
378C4—1722no—
379C4C22×C8×D4311yescharacteristic
380C4#131×D4311yescharacteristic
381C4#1458369812yes—
382C2—862no—
383C2—1724no—
384C2C8×D4×D4311yescharacteristic
385C2#1914339411yescharacteristic
386C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC43×#1579C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063348C4
cosocleC42×C43C24
hypercenter#1579D43
hypocenterC43#17849
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
1. C8×#10621902C2semidirect
3. #19133420C2semidirect
4. #19133418C2semidirect
5. #19133414C2semidirect
6. #19133410C2semidirect
7. #19133405C2semidirect
8. #19133340C2semidirect
9. #19132976C2semidirect
10. #322×D43C2semidirect
11. C43×#1579C2semidirect
46. #13063348C8semidirect
95. #10621902C2×C8semidirect
104. Q16×C43C2×C8semidirect
114. #10621884C2×C8semidirect
130. D344C2×C8semidirect
136. C8×D43C2×C8semidirect
194. #1579D43semidirect
238. C43#17849semidirect
298. Q16C8×D43semidirect

Maximal subgroups

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

subgroupindex
C8×#106219022
C4×#130633482
#191334202
#191334182
#191334142
#191334102
#191334052
#191333402
#191329762
#322×D432
C43×#15792
#1784943