Finite Group Databasebeta

← D4×#14558993 #34080808

Subgroups — D4×#14558993 #34080808

Order 19328.

546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14558993C212yesmaximal, complemented
2D4×Dic302C211yesmaximal, characteristic, complemented
3D4×D604C211yesmaximal, characteristic
4#23752585C211yesmaximal, characteristic, complemented
5#23752441C212yesmaximal, complemented
6#23752418C211yesmaximal, characteristic, complemented
7#23752413C211yesmaximal, characteristic, complemented
8#23752365C212yesmaximal, complemented
9#23752353C212yesmaximal, complemented
10C4×#14558993C211yesmaximal, characteristic, complemented
11C8×D4×C151C211yesmaximal, characteristic, complemented
12C22×Dic302C2212yescomplemented
13C22×D604C2212yes—
14C2×D4×D151—21no—
15C2×#14558993—28no—
16C2×#14558993C2212yes—
17C2×#14558993C2211yescharacteristic
18C2×#14558993C2212yescomplemented
19C2×#14558993C2212yescomplemented
20C2×#14558993C2212yescomplemented
21#18012739C2211yescharacteristic, complemented
22#18012738—21no—
23#18012736C2211yescharacteristic
24#18012718C2212yescomplemented
25#18012716—22no—
26#18012714—21no—
27#18012713C2212yes—
28#18012709—22no—
29C4×Dic302C2211yescharacteristic, complemented
30C4×D604C2211yescharacteristic
31D4×Dic151—21no—
32#18012671C2211yescharacteristic, complemented
33#18012664C2211yescharacteristic, complemented
34#18012664C2212yescomplemented
35#18012661C2211yescharacteristic
36#18012661C2212yescomplemented
37C22×C8×C151C2212yescomplemented
38C4×D4×C151C2211yescharacteristic
39C4⋊C8×C151C2211yescharacteristic, complemented
40C22⋊C8×C151C2212yescomplemented
41C4×C8×C151C2211yescharacteristic, complemented
42C23×D151—22no—
43C2×Dic302—24no—
44C2×Dic302—22no—
45C2×Dic302—42no—
46C2×Dic302C2312yes—
47C2×Dic302C2311yescharacteristic
48C2×D604—24no—
49C2×D604—22no—
50C2×D604—21no—
51C2×D604—21no—
52C2×D604—42no—
53C2×D604C2312yes—
54C2×D604C2311yescharacteristic
55C2×C22⋊D151—22no—
56D4×D151—44no—
57C22×Dic151—22no—
58C2×C4×D151—21no—
59#14558993—24no—
60#14558993—24no—
61#14558993—24no—
62#14558993—42no—
63#14558993D414yesdirect product factor
64C4⋊Dic151—21no—
65C4⋊Dic151—21no—
66C4⋊Dic151C2311yescharacteristic
67C4⋊Dic151C2311yescharacteristic
68Dic151⋊C4—21no—
69Dic151⋊C4—22no—
70C22⋊Dic151—22no—
71(C2×D151)⋊C4—21no—
72(C2×D151)⋊C4—22no—
73C4×Dic151—21no—
74C2×D4×C151D411yescharacteristic
75C22×C4×C151C2312yes—
76C2×C8×C151—24no—
77C2×C8×C151C2312yes—
78C2×C8×C151C2311yescharacteristic
79C2×C8×C151C2311yescharacteristic
80C4⋊C4×C151D411yescharacteristic
81C22⋊C4×C151D412yes—
82C42×C151C2311yescharacteristic
83C22×D151—21no—
84C22×D151—22no—
85C22×D151—44no—
86C22×D151—44no—
87C22×D151—82no—
88Dic302—21no—
89Dic302—22no—
90Dic302—22no—
91Dic302—44no—
92Dic302C2×D412yescomplemented
93D604—22no—
94D604—21no—
95D604—22no—
96D604—44no—
97D604—42no—
98D604—81no—
99D604C2×D412yes—
100C22⋊D151—44no—
101C2×Dic151—21no—
102C2×Dic151—21no—
103C2×Dic151—21no—
104C2×Dic151—22no—
105C2×Dic151—44no—
106C4×D151—42no—
107C23×C151C2×D412yes—
108D4×C151SD1614yescomplemented
109C2×C4×C151—22no—
110C2×C4×C151—22no—
111C2×C4×C151C2×D411yescharacteristic
112C2×C4×C151C2×D412yes—
113C2×C4×C151C2×D411yescharacteristic
114C2×C4×C151C2411yescharacteristic
115C8×C151—22no—
116C8×C151—21no—
117C8×C151C2×D412yescomplemented
118C22×C151—22no—
119C22×C151—22no—
120C22×C151C2×SD1614yescomplemented
121C22×C151C22×D411yescharacteristic
122C2×D151—22no—
123C2×D151—41no—
124C2×D151—41no—
125C2×D151—42no—
126C2×D151—42no—
127C2×D151—42no—
128C2×D151—88no—
129C4×C151—22no—
130C4×C151—21no—
131C4×C151C2×SD1612yescomplemented
132C4×C151C22×D411yescharacteristic
133C4×C151H(5,𝔽2)11yescharacteristic
134Dic151—22no—
135Dic151—42no—
136Dic151—41no—
137Dic151—41no—
138C2×C151—24no—
139C2×C151D4211yescharacteristic
140C2×C151C22×SD1611yescharacteristic
141C2×C151#57711yescharacteristic
142D151—42no—
143D151—82no—
144C151D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—1511nomaximal, Sylow
146C22×SD16—1512no—
147D4×Q8—1511no—
148D42—1511no—
149#492—1511no—
150#465—1512no—
151#461—1511no—
152#460—1511no—
153#450—1512no—
154#448—1512no—
155C4×SD16—1511no—
156C8×D4D15111yescharacteristic, complemented
157C22×Q8—1512no—
158C22×D4—3021no—
159C22×D4—1512no—
160C2×SD16—3028no—
161C2×SD16—1512no—
162C2×SD16—1512no—
163C2×SD16—1512no—
164C2×SD16—1512no—
165C2×SD16—1511no—
166C22×C8C2×D15112yescomplemented
167C4⋊Q8—3021no—
168C4⋊Q8—1511no—
169#127—1511no—
170C22⋊Q8—3022no—
171C22⋊Q8—1512no—
172#121—3021no—
173#121—1512no—
174#120—3022no—
175C4×Q8—1511no—
176C4×D4—3021no—
177C4×D4—1511no—
178C4×D4C2×D15111yescharacteristic
179#106—1511no—
180C4⋊C8C2×D15111yescharacteristic, complemented
181#103—1511no—
182#103—1512no—
183#102—1511no—
184#102—1512no—
185C22⋊C8C2×D15112yescomplemented
186C4×C8C2×D15111yescharacteristic, complemented
187C24—3022no—
188C2×Q8—3024no—
189C2×Q8—3022no—
190C2×Q8—6042no—
191C2×Q8—1512no—
192C2×Q8—1511no—
193C2×D4—3024no—
194C2×D4—3022no—
195C2×D4—3022no—
196C2×D4—3021no—
197C2×D4—3021no—
198C2×D4—6042no—
199C2×D4—6044no—
200C2×D4—1512no—
201C2×D4—1511no—
202C2×D4D60411yescharacteristic
203C22×C4—3022no—
204C22×C4—3021no—
205C22×C4C22×D15112yes—
206SD16—3024no—
207SD16—3024no—
208SD16—3024no—
209SD16—6042no—
210SD16—1514no—
211C2×C8—24no—
212C2×C8C22×D15111yescharacteristic
213C2×C8C22×D15112yes—
214C2×C8C22×D15111yescharacteristic
215C4⋊C4—3021no—
216C4⋊C4—3022no—
217C4⋊C4—3021no—
218C4⋊C4—3021no—
219C4⋊C4—1511no—
220C4⋊C4—1511no—
221C4⋊C4D60411yescharacteristic
222C22⋊C4—3022no—
223C22⋊C4—3021no—
224C22⋊C4—3022no—
225C22⋊C4D60412yes—
226C42—3021no—
227C42C22×D15111yescharacteristic
228C23—3021no—
229C23—3022no—
230C23—6044no—
231C23—6044no—
232C23—12082no—
233C23C2×D60412yes—
234Q8—3021no—
235Q8—3022no—
236Q8—3022no—
237Q8—6044no—
238Q8—1512no—
239D4—3022no—
240D4—3021no—
241D4—3022no—
242D4—6044no—
243D4—6044no—
244D4—6042no—
245D4—1512no—
246D4—12081no—
247D4#1455899314yesdirect product factor
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—3021no—
251C2×C4—3021no—
252C2×C4—3021no—
253C2×C4—3022no—
254C2×C4—6044no—
255C2×C4—6042no—
256C2×C4C2×D60411yescharacteristic
257C2×C4C2×D60412yes—
258C2×C4C2×D60411yescharacteristic
259C2×C4C23×D15111yescharacteristic
260C8—22no—
261C8—21no—
262C8D4×D15112yescomplemented
263C22—22no—
264C22—22no—
265C22—3022no—
266C22—6041no—
267C22—6041no—
268C22—6042no—
269C22—6042no—
270C22—6042no—
271C22—12088no—
272C22C2×#1455899314yescomplemented
273C22C22×D60411yescharacteristic
274C4—21no—
275C4—22no—
276C4—3022no—
277C4—6041no—
278C4—6041no—
279C4—6042no—
280C4C2×#1455899312yescomplemented
281C4C2×D4×D15111yescharacteristic
282C4#1801278511yescharacteristic
283C2—24no—
284C2—6042no—
285C2—12082no—
286C2D4×D60411yescharacteristic
287C2C22×#1455899311yescharacteristic
288C2#2375302411yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC8×D4×C151C2
socleC22×C151C22×D4
prime radicalD4×D604C2
hypercenterC8×D4D151
hypocenterC151D4×SD16
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14558993C2semidirect
2. D4×Dic302C2semidirect
4. #23752585C2semidirect
5. #23752441C2semidirect
6. #23752418C2semidirect
7. #23752413C2semidirect
8. #23752365C2semidirect
9. #23752353C2semidirect
10. C4×#14558993C2semidirect
11. C8×D4×C151C2semidirect
12. C22×Dic302C22semidirect
18. C2×#14558993C22semidirect
19. C2×#14558993C22semidirect
20. C2×#14558993C22semidirect
21. #18012739C22semidirect
24. #18012718C22semidirect
29. C4×Dic302C22semidirect
32. #18012671C22semidirect
33. #18012664C22semidirect
34. #18012664C22semidirect
36. #18012661C22semidirect
37. C22×C8×C151C22semidirect
39. C4⋊C8×C151C22semidirect
40. C22⋊C8×C151C22semidirect
41. C4×C8×C151C22semidirect
63. #14558993D4direct (N × H)
92. Dic302C2×D4semidirect
108. D4×C151SD16semidirect
117. C8×C151C2×D4semidirect
120. C22×C151C2×SD16semidirect
131. C4×C151C2×SD16semidirect
144. C151D4×SD16semidirect
156. C8×D4D151semidirect
166. C22×C8C2×D151semidirect
180. C4⋊C8C2×D151semidirect
185. C22⋊C8C2×D151semidirect
186. C4×C8C2×D151semidirect
247. D4#14558993direct (N × H)
262. C8D4×D151semidirect
272. C22C2×#14558993semidirect
280. C4C2×#14558993semidirect

Maximal subgroups

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

subgroupindex
C22×#145589932
D4×Dic3022
D4×D6042
#237525852
#237524412
#237524182
#237524132
#237523652
#237523532
C4×#145589932
C8×D4×C1512
D4×SD16151