Finite Group Databasebeta

← D8×#625 #11885760

Subgroups — D8×#625 #11885760

Order 1152.

1307 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 1307 conjugacy classes of subgroups — too many to draw. Only its 200 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×C3×D3×D8C212yesmaximal, complemented
2D4×#625C212yesmaximal, complemented
3D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10591486C212yesmaximal, complemented
5#10591447C214yesmaximal, complemented
6#10590886C211yesmaximal, characteristic, complemented
7#10590831C212yesmaximal, complemented
8C8×#625C211yesmaximal, characteristic, complemented
9D8×#67—32nomaximal
10C2×C3×D3×D4C2214yescomplemented
11C22×#625—22no—
12C2×C32×D8C2211yescharacteristic
13D4×C3⋊Dic3C2212yescomplemented
14C2×C3×#213C2214yescomplemented
15C3×D3×D8—28no—
16C2×C3×D24C2212yescomplemented
17C2×C3×D3×C8C2212yescomplemented
18#63980—22no—
19#63976—24no—
20#63914C2212yescomplemented
21#63908C2214yescomplemented
22C4×#625C2211yescharacteristic
23C2×#3713C2212yescomplemented
24#63659C2212yescomplemented
25#63645C2211yescharacteristic, complemented
26C8×C3⋊Dic3C2211yescharacteristic, complemented
27#63572C2211yescharacteristic, complemented
28#63563C2214yescomplemented
29(C2×D3)⋊(C3⋊C8)C2212yescomplemented
30C22×C3×D8—32no—
31D4×#67—34no—
32C2×D3×D8D312yescomplemented
33#5217—34no—
34#5157—32no—
35#5156—34no—
36#5151—32no—
37#5150—34no—
38Dic3×D8—32no—
39Dic3×D8—61no—
40#5115—32no—
41C8×#67—32no—
42C23×C3×D3—24no—
43C2×C32×D4C2312yes—
44C22×C3⋊Dic3—22no—
45C2×C3×#67—24no—
46C3×D3×D4—28no—
47C3×D3×D4—44no—
48C2×C3×D12C2314yes—
49C2×C3×C4×D3C2312yes—
50C2×#625—24no—
51C2×#625—22no—
52C2×#625—22no—
53C2×#625—48no—
54C2×#625D411yescharacteristic
55C32×D8D414yescomplemented
56C2×C32×C8C2311yescharacteristic
57#3757—22no—
58C4⋊(C3⋊Dic3)C2312yes—
59C4×C3⋊Dic3C2311yescharacteristic
60C2×C3⋊(C3⋊C8)C2311yescharacteristic
61C3×#213—28no—
62C2×C3×C3⋊C8C2312yes—
63C3×D24—24no—
64C3×D3×C8—24no—
65#3724D411yescharacteristic
66(C2×D3)⋊Dic3—24no—
67(C2×D3)⋊Dic3D412yes—
68#3713—42no—
69D4×D8—91noSylow
70C22×C3×D4—34no—
71C22×#67—64no—
72C2×D3×D4C2×D314yescomplemented
73C2×C3×D8—21no—
74C2×C3×D8—34no—
75C2×C3×D8—32no—
76C2×C3×D8—68no—
77C2×C3×D8C2×D312yes—
78C22×C3×C8—32no—
79#953—64no—
80#940—34no—
81#939—64no—
82#938—34no—
83#937—64no—
84D4×Dic3—34no—
85D4×Dic3—62no—
86C2×#213—34no—
87C2×#213C2×D314yescomplemented
88#930—34no—
89C4×#67—32no—
90D3×D8—28no—
91C2×D24C2×D312yescomplemented
92C2×D3×C8C2×D312yescomplemented
93#832—34no—
94#832—34no—
95#832—62no—
96#830—32no—
97#821—34no—
98(C2×D3)⋊C8—32no—
99#818—32no—
100#818—61no—
101Dic3⋊C8—32no—
102C8×Dic3—32no—
103C8×Dic3—61no—
104C23×C32—22no—
105C22×C3×D3—24no—
106C22×C3×D3—48no—
107C22×C3×D3—48no—
108C22×C3×D3—84no—
109C22×C3×D3C2×D412yes—
110C32×D4—22no—
111C32×D4C2×D414yescomplemented
112C2×C32×C4C2411yescharacteristic
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—44no—
115C2×C3⋊Dic3C2×D411yescharacteristic
116C2×C3⋊Dic3C2×D411yescharacteristic
117C3×#67—48no—
118C2×C3×Dic3C2×D412yes—
119C3×D12—24no—
120C3×D12—24no—
121C3×C4×D3—22no—
122C3×C4×D3—22no—
123#625—48no—
124#625—44no—
125#625—82no—
126#625D814yesdirect product factor
127C32×C8C2×D412yescomplemented
128C3⋊(C3⋊C8)—21no—
129C3×C3⋊C8—22no—
130C22×D8—32no—
131D42—92no—
132#493—91no—
133#466—92no—
134#459—92no—
135#447—94no—
136C4×D8—91no—
137C8×D4—91no—
138C24×C3—64no—
139C23×D3—24no—
140C2×C3×D4—22no—
141C2×C3×D4—34no—
142C2×C3×D4—64no—
143C2×C3×D4—68no—
144C2×C3×D4—124no—
145C2×C3×D4C22×D314yes—
146C22×C3×C4—32no—
147C2×#67—24no—
148C2×#67—32no—
149C2×#67—64no—
150C2×#67—64no—
151C2×#67—64no—
152C2×#67—64no—
153C2×#67—1216no—
154C22×Dic3—64no—
155C22×Dic3—122no—
156D3×D4—28no—
157D3×D4—44no—
158C2×D12C22×D314yes—
159C2×C4×D3C22×D312yes—
160C3×D8—24no—
161C3×D8—68no—
162C3×D8—64no—
163C3×D8#6718yescomplemented
164C2×C3×C8—21no—
165C2×C3×C8—32no—
166C2×C3×C8—64no—
167C2×C3×C8C22×D312yes—
168#217—32no—
169#217—64no—
170#217—64no—
171#217—122no—
172#213—28no—
173#213—124no—
174(C2×D3)⋊C4—32no—
175(C2×D3)⋊C4—64no—
176C4⋊Dic3—34no—
177C4⋊Dic3—62no—
178Dic3⋊C4—32no—
179C4×Dic3—32no—
180C4×Dic3—61no—
181C2×C3⋊C8—32no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8C22×D312yes—
184D24—24no—
185D3×C8—24no—
186C22×C32—24no—
187C22×C32—42no—
188C22×C32—42no—
189C22×C32C22×D411yescharacteristic
190C2×C3×D3—22no—
191C2×C3×D3—22no—
192C2×C3×D3—44no—
193C2×C3×D3—44no—
194C2×C3×D3—44no—
195C2×C3×D3—816no—
196C2×C3×D3C2×D814yescomplemented
197C32×C4C22×D411yescharacteristic
198C32×C4H(5,𝔽2)11yescharacteristic
199C3⋊Dic3—21no—
200C3⋊Dic3—42no—
201C3⋊Dic3C2×D812yescomplemented
202C3×Dic3—22no—
203C22×D4—34no—
204C22×D4—182no—
205C2×D8—34no—
206C2×D8—32no—
207C2×D8—68no—
208C2×D8—92no—
209C2×D8D3211yescharacteristic
210C22×C8—32no—
211#127—92no—
212#121—94no—
213#121—182no—
214#120—184no—
215C4×D4—91no—
216C4×D4—92no—
217#107—91no—
218C4⋊C8—91no—
219#102—94no—
220#102—92no—
221C22⋊C8—92no—
222C4×C8—91no—
223C23×C3—24no—
224C23×C3—32no—
225C23×C3—42no—
226C23×C3—64no—
227C23×C3—128no—
228C23×C3—128no—
229C23×C3—244no—
230C22×D3—24no—
231C22×D3—48no—
232C22×D3—48no—
233C22×D3—84no—
234C22×D3D3×D412yes—
235C3×D4—24no—
236C3×D4—24no—
237C3×D4—42no—
238C3×D4—64no—
239C3×D4—64no—
240C3×D4—128no—
241C3×D4C2×#6718yescomplemented
242C2×C3×C4—21no—
243C2×C3×C4—32no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4C23×D312yes—
247#67—38no—
248#67—48no—
249#67—128no—
250#67—128no—
251#67—128no—
252#67—244no—
253C2×Dic3—32no—
254C2×Dic3—32no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—64no—
258C2×Dic3—122no—
259C2×Dic3—128no—
260C2×Dic3—244no—
261C2×Dic3D3×D412yes—
262D12—24no—
263D12—24no—
264C4×D3—22no—
265C4×D3—22no—
266C3×C8—22no—
267C3×C8—62no—
268C3×C8C2×#6714yescomplemented
269C3⋊C8—22no—
270C3⋊C8—62no—
271C3⋊C8—121no—
272C2×C32—44no—
273C2×C32D4211yescharacteristic
274C2×C32C22×D811yescharacteristic
275C2×C32#57611yescharacteristic
276C3×D3—24no—
277C3×D3—84no—
278C24—64no—
279C2×D4—34no—
280C2×D4—64no—
281C2×D4—68no—
282C2×D4—91no—
283C2×D4—124no—
284C2×D4—182no—
285C2×D4—182no—
286C2×D4—184no—
287C2×D4—368no—
288C2×D4C2×D3212yes—
289C22×C4—32no—
290C22×C4—182no—
291D8—68no—
292D8—64no—
293D8—362no—
294D8#62514yesdirect product factor
295C2×C8—32no—
296C2×C8—64no—
297C2×C8—91no—
298C2×C8C2×D3211yescharacteristic
299C4⋊C4—91no—
300C4⋊C4—92no—
301C22⋊C4—92no—
302C22⋊C4—184no—
303C22⋊C4—182no—
304C42—91no—
305C22×C3—28no—
306C22×C3—21no—
307C22×C3—34no—
308C22×C3—44no—
309C22×C3—44no—
310C22×C3—44no—
311C22×C3—62no—
312C22×C3—62no—
313C22×C3—82no—
314C22×C3—82no—
315C22×C3—124no—
316C22×C3—124no—
317C22×C3—124no—
318C22×C3—2416no—
319C22×C3C2×D3×D412yes—
320C2×D3—22no—
321C2×D3—22no—
322C2×D3—44no—
323C2×D3—44no—
324C2×D3—44no—
325C2×D3—816no—
326C2×D3D3×D814yescomplemented
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—62no—
330C3×C4#100412yes—
331C3×C4C22×#6712yes—
332Dic3—22no—
333Dic3—34no—
334Dic3—62no—
335Dic3—62no—
336Dic3—121no—
337Dic3—124no—
338Dic3—242no—
339C32D4×D811yescharacteristic, complemented, Sylow
340C23—22no—
341C23—32no—
342C23—64no—
343C23—128no—
344C23—128no—
345C23—244no—
346D4—22no—
347D4—64no—
348D4—64no—
349D4—94no—
350D4—128no—
351D4—364no—
352D4—368no—
353D4—722no—
354D4C2×#62514yescomplemented
355C2×C4—32no—
356C2×C4—62no—
357C2×C4—62no—
358C2×C4—91no—
359C2×C4—91no—
360C2×C4—182no—
361C2×C4—364no—
362C2×C4C22×D3211yescharacteristic
363C8—62no—
364C8—181no—
365C8C2×#62512yescomplemented
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—48no—
370C2×C3—64no—
371C2×C3—84no—
372C2×C3—244no—
373C2×C3C2×D3×D812yes—
374C2×C3#575712yes—
375C2×C3D4×#6712yes—
376D3—24no—
377D3—84no—
378C22—24no—
379C22—34no—
380C22—42no—
381C22—42no—
382C22—62no—
383C22—62no—
384C22—124no—
385C22—124no—
386C22—124no—
387C22—2416no—
388C22D32×D411yescharacteristic
389C4—62no—
390C4—92no—
391C4—181no—
392C4—362no—
393C4#6431311yescharacteristic
394C4C22×#62511yescharacteristic
395C3—21no—
396C3D8×#6712yescomplemented
397C2—44no—
398C2—64no—
399C2—244no—
400C2D32×D811yescharacteristic
401C2#1059473111yescharacteristic
402C2D4×#62511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D8C2semidirect
2. D4×#625C2semidirect
3. D8×C3⋊Dic3C2semidirect
4. #10591486C2semidirect
5. #10591447C2semidirect
6. #10590886C2semidirect
7. #10590831C2semidirect
8. C8×#625C2semidirect
10. C2×C3×D3×D4C22semidirect
13. D4×C3⋊Dic3C22semidirect
14. C2×C3×#213C22semidirect
16. C2×C3×D24C22semidirect
17. C2×C3×D3×C8C22semidirect
20. #63914C22semidirect
21. #63908C22semidirect
23. C2×#3713C22semidirect
24. #63659C22semidirect
25. #63645C22semidirect
26. C8×C3⋊Dic3C22semidirect
27. #63572C22semidirect
28. #63563C22semidirect
29. (C2×D3)⋊(C3⋊C8)C22semidirect
32. C2×D3×D8D3semidirect
55. C32×D8D4semidirect
72. C2×D3×D4C2×D3semidirect
87. C2×#213C2×D3semidirect
91. C2×D24C2×D3semidirect
92. C2×D3×C8C2×D3semidirect
111. C32×D4C2×D4semidirect
126. #625D8direct (N × H)
127. C32×C8C2×D4semidirect
163. C3×D8#67semidirect
196. C2×C3×D3C2×D8semidirect
201. C3⋊Dic3C2×D8semidirect
241. C3×D4C2×#67semidirect
268. C3×C8C2×#67semidirect
294. D8#625direct (N × H)
326. C2×D3D3×D8semidirect
339. C32D4×D8semidirect
354. D4C2×#625semidirect
365. C8C2×#625semidirect
396. C3D8×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
D4×#6252
D8×C3⋊Dic32
#105914862
#105914472
#105908862
#105908312
C8×#6252
D8×#673