Finite Group Databasebeta

← D4×#3774 #11885781

Subgroups — D4×#3774 #11885781

Order 1152.

1048 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C22×#3774C212yesmaximal, complemented
2D4×#625C212yesmaximal, complemented
3D4×#622C211yesmaximal, characteristic, complemented
4#10593520C212yesmaximal, complemented
5#10593519C214yesmaximal, complemented
6#10593418C211yesmaximal, characteristic, complemented
7#10593417C212yesmaximal, complemented
8C4×#3774C211yesmaximal, characteristic, complemented
9C2×C3×D3×D4—22no—
10C22×#625C2214yescomplemented
11C22×#622C2212yescomplemented
12C2×#3774—28no—
13C2×#3774C2211yescharacteristic
14C2×#3774C2214yescomplemented
15C2×#3774C2212yescomplemented
16C2×#3774C2212yescomplemented
17D4×C3⋊Dic3C2211yescharacteristic
18#63980C2214yescomplemented
19#63976—24no—
20#63914C2212yescomplemented
21#63908—22no—
22C4×#625C2212yescomplemented
23C22⋊#622C2212yescomplemented
24C4⋊#622C2211yescharacteristic, complemented
25C4×#622C2211yescharacteristic, complemented
26#63743C2211yescharacteristic, complemented
27#63739C2212yescomplemented
28#63739C2214yescomplemented
29D4×#67—62no—
30C23×C3×D3—24no—
31C2×C32×D4D411yescharacteristic
32C22×C3⋊Dic3C2312yes—
33C2×C3×#67—24no—
34C3×D3×D4—48no—
35C2×C3×D12—22no—
36C2×C3×C4×D3—22no—
37C2×#625—28no—
38C2×#625—24no—
39C2×#625—22no—
40C2×#625—44no—
41C2×#625C2314yes—
42C2×#625C2312yes—
43C2×#622—24no—
44C2×#622C2311yescharacteristic
45C2×#622C2312yes—
46C2×#622C2311yescharacteristic
47#3774—28no—
48#3774—24no—
49#3774—42no—
50#3774D414yesdirect product factor
51#3757D412yes—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53C4×C3⋊Dic3C2311yescharacteristic
54#3724C2312yes—
55(C2×D3)⋊Dic3—22no—
56(C2×D3)⋊Dic3—24no—
57D4×D8—91nomaximal, Sylow
58C22×C3×D4—62no—
59C22×#67—64no—
60C2×D3×D4—22no—
61#953—64no—
62#940—62no—
63#939—64no—
64#938—62no—
65#937—64no—
66D4×Dic3—62no—
67#930—62no—
68C4×#67—62no—
69C23×C32C2×D412yes—
70C22×C3×D3—22no—
71C22×C3×D3—24no—
72C22×C3×D3—48no—
73C22×C3×D3—48no—
74C22×C3×D3—84no—
75C32×D4D814yescomplemented
76C2×C32×C4C2×D411yescharacteristic
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3C2×D411yescharacteristic
80C2×C3⋊Dic3C2×D412yes—
81C2×C3⋊Dic3C2411yescharacteristic
82C3×#67—48no—
83C2×C3×Dic3—22no—
84C3×D12—44no—
85C3×C4×D3—44no—
86#625—22no—
87#625—24no—
88#625—24no—
89#625—48no—
90#625—82no—
91#625C2×D414yescomplemented
92#622—22no—
93#622—21no—
94#622C2×D412yescomplemented
95C22×D8—92no—
96D42—92no—
97#493—91no—
98#466—92no—
99#459—92no—
100#447—94no—
101C4×D8—91no—
102C8×D4—91no—
103C24×C3—64no—
104C23×D3—24no—
105C2×C3×D4—22no—
106C2×C3×D4—62no—
107C2×C3×D4—64no—
108C2×C3×D4—128no—
109C22×C3×C4—62no—
110C2×#67—24no—
111C2×#67—62no—
112C2×#67—64no—
113C2×#67—64no—
114C2×#67—64no—
115C2×#67—64no—
116C2×#67—128no—
117C2×#67—128no—
118C22×Dic3—64no—
119D3×D4—48no—
120C2×D12—22no—
121C2×C4×D3—22no—
122#217—64no—
123#217—62no—
124#217—64no—
125(C2×D3)⋊C4—62no—
126(C2×D3)⋊C4—64no—
127C4⋊Dic3—62no—
128Dic3⋊C4—62no—
129C4×Dic3—62no—
130C22×C32—22no—
131C22×C32—22no—
132C22×C32C2×D814yescomplemented
133C22×C32C22×D411yescharacteristic
134C2×C3×D3—24no—
135C2×C3×D3—42no—
136C2×C3×D3—42no—
137C2×C3×D3—44no—
138C2×C3×D3—44no—
139C2×C3×D3—44no—
140C2×C3×D3—816no—
141C32×C4C2×D812yescomplemented
142C3⋊Dic3—22no—
143C3⋊Dic3—21no—
144C3⋊Dic3C22×D411yescharacteristic
145C3⋊Dic3H(5,𝔽2)11yescharacteristic
146C3×Dic3—42no—
147C22×D4—62no—
148C22×D4—94no—
149C2×D8—91no—
150C2×D8—94no—
151C2×D8—92no—
152C2×D8—92no—
153C2×D8—188no—
154C22×C8—92no—
155#127—92no—
156#121—94no—
157#121—182no—
158#120—184no—
159C4×D4—91no—
160C4×D4—92no—
161#107—91no—
162C4⋊C8—91no—
163#102—92no—
164#102—94no—
165C22⋊C8—92no—
166C4×C8—91no—
167C23×C3—24no—
168C23×C3—62no—
169C23×C3—64no—
170C23×C3—128no—
171C23×C3—128no—
172C23×C3—244no—
173C22×D3—22no—
174C22×D3—24no—
175C22×D3—48no—
176C22×D3—48no—
177C22×D3—84no—
178C3×D4—28no—
179C3×D4—124no—
180C3×D4—128no—
181C2×C3×C4—22no—
182C2×C3×C4—62no—
183C2×C3×C4—124no—
184#67—48no—
185#67—64no—
186#67—64no—
187#67—124no—
188#67—124no—
189#67—128no—
190#67—128no—
191#67—244no—
192C2×Dic3—22no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—64no—
196C2×Dic3—124no—
197C2×Dic3—124no—
198D12—44no—
199C4×D3—44no—
200C2×C32—24no—
201C2×C32D4211yescharacteristic
202C2×C32C22×D811yescharacteristic
203C2×C32#57611yescharacteristic
204C3×D3—44no—
205C3×D3—84no—
206C24—64no—
207C2×D4—64no—
208C2×D4—62no—
209C2×D4—92no—
210C2×D4—94no—
211C2×D4—128no—
212C2×D4—184no—
213C2×D4—182no—
214C2×D4—188no—
215C2×D4—364no—
216C2×D4GO+(4,𝔽2)11yescharacteristic
217C22×C4—62no—
218C22×C4—92no—
219D8—94no—
220D8—184no—
221D8—188no—
222D8—362no—
223C2×C8—91no—
224C2×C8—91no—
225C2×C8—92no—
226C2×C8—184no—
227C4⋊C4—92no—
228C4⋊C4—91no—
229C22⋊C4—92no—
230C22⋊C4—182no—
231C22⋊C4—184no—
232C42—91no—
233C22×C3—22no—
234C22×C3—28no—
235C22×C3—44no—
236C22×C3—44no—
237C22×C3—64no—
238C22×C3—122no—
239C22×C3—122no—
240C22×C3—124no—
241C22×C3—124no—
242C22×C3—124no—
243C22×C3—2416no—
244C2×D3—24no—
245C2×D3—42no—
246C2×D3—42no—
247C2×D3—44no—
248C2×D3—44no—
249C2×D3—44no—
250C2×D3—816no—
251C3×C4—24no—
252C3×C4—122no—
253Dic3—42no—
254Dic3—62no—
255Dic3—62no—
256Dic3—124no—
257Dic3—122no—
258C32D4×D811yescharacteristic, complemented, Sylow
259C23—62no—
260C23—64no—
261C23—128no—
262C23—128no—
263C23—244no—
264C23C2×GO+(4,𝔽2)12yes—
265D4—94no—
266D4—128no—
267D4—124no—
268D4—182no—
269D4—184no—
270D4—184no—
271D4—368no—
272D4—722no—
273D4#377414yesdirect product factor
274C2×C4—62no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—92no—
278C2×C4—124no—
279C2×C4—182no—
280C2×C4—182no—
281C2×C4C2×GO+(4,𝔽2)11yescharacteristic
282C8—92no—
283C8—182no—
284C8—181no—
285C2×C3—22no—
286C2×C3—22no—
287C2×C3—22no—
288C2×C3—48no—
289C2×C3—124no—
290C2×C3—244no—
291D3—44no—
292D3—84no—
293C22—22no—
294C22—22no—
295C22—64no—
296C22—122no—
297C22—122no—
298C22—124no—
299C22—124no—
300C22—124no—
301C22—2416no—
302C22C2×#377414yescomplemented
303C22C22×GO+(4,𝔽2)11yescharacteristic
304C4—91no—
305C4—91no—
306C4—122no—
307C4—181no—
308C4—182no—
309C4C2×#377412yescomplemented
310C3—22no—
311C2—24no—
312C2—124no—
313C2—244no—
314C2#1059651411yescharacteristic
315C2D4×GO+(4,𝔽2)11yescharacteristic
316C2C22×#377411yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC2×C32×D4D4
socleC22×C32C22×D4
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32D4×D8
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3774C2semidirect
2. D4×#625C2semidirect
3. D4×#622C2semidirect
4. #10593520C2semidirect
5. #10593519C2semidirect
6. #10593418C2semidirect
7. #10593417C2semidirect
8. C4×#3774C2semidirect
10. C22×#625C22semidirect
11. C22×#622C22semidirect
14. C2×#3774C22semidirect
15. C2×#3774C22semidirect
16. C2×#3774C22semidirect
18. #63980C22semidirect
20. #63914C22semidirect
22. C4×#625C22semidirect
23. C22⋊#622C22semidirect
24. C4⋊#622C22semidirect
25. C4×#622C22semidirect
26. #63743C22semidirect
27. #63739C22semidirect
28. #63739C22semidirect
50. #3774D4direct (N × H)
75. C32×D4D8semidirect
91. #625C2×D4semidirect
94. #622C2×D4semidirect
132. C22×C32C2×D8semidirect
141. C32×C4C2×D8semidirect
258. C32D4×D8semidirect
273. D4#3774direct (N × H)
302. C22C2×#3774semidirect
309. C4C2×#3774semidirect

Maximal subgroups

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

subgroupindex
C22×#37742
D4×#6252
D4×#6222
#105935202
#105935192
#105934182
#105934172
C4×#37742
D4×D89