Finite Group Databasebeta

← D8×C22⋊D19 #14575306

Subgroups — D8×C22⋊D19 #14575306

Order 2432.

620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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×D8×D19C211yesmaximal, characteristic, complemented
2D4×C22⋊D19C212yesmaximal, complemented
3#11926919C211yesmaximal, characteristic, complemented
4#11926780C211yesmaximal, characteristic, complemented
5#11926777C211yesmaximal, characteristic, complemented
6#11926737C212yesmaximal, complemented
7#11926678C212yesmaximal, complemented
8#11926676C212yesmaximal, complemented
9D8×Dic19C211yesmaximal, characteristic, complemented
10C8×C22⋊D19C211yesmaximal, characteristic, complemented
11C22×D8×C19C211yesmaximal, characteristic, complemented
12C22×D4×C19C2212yescomplemented
13C22×C22⋊D19—22no—
14C2×D4×D19C2212yescomplemented
15C2×D8×C19—24no—
16C2×D8×C19C2211yescharacteristic
17C2×D8×C19C2211yescharacteristic, complemented
18C2×D8×C19C2212yescomplemented
19C22×C8×C19C2211yescharacteristic, complemented
20#10597399—22no—
21#10597386C2212yescomplemented
22#10597385—22no—
23#10597384C2212yescomplemented
24#10597383—22no—
25D4×Dic19C2212yescomplemented
26C2×#64525C2212yescomplemented
27C2×#64525C2212yescomplemented
28#10597376C2212yescomplemented
29C4×C22⋊D19C2211yescharacteristic
30D8×D19—24no—
31C2×D152C2211yescharacteristic, complemented
32C2×C8×D19C2211yescharacteristic, complemented
33#10597289C2212yescomplemented
34#10597289C2212yescomplemented
35C22⋊(C19⋊C8)C2211yescharacteristic, complemented
36#10597278C2212yescomplemented
37(C2×D19)⋊C8C2211yescharacteristic, complemented
38#10597275C2211yescharacteristic, complemented
39Dic19⋊C8C2211yescharacteristic, complemented
40C8×Dic19C2211yescharacteristic, complemented
41C24×C19—22no—
42C23×D19—22no—
43C2×D4×C19—24no—
44C2×D4×C19—22no—
45C2×D4×C19—42no—
46C2×D4×C19C2312yes—
47C2×D4×C19C2312yes—
48C22×C4×C19C2311yescharacteristic
49C2×C22⋊D19—22no—
50C2×C22⋊D19—22no—
51C2×C22⋊D19—22no—
52C2×C22⋊D19—22no—
53C2×C22⋊D19—22no—
54C2×C22⋊D19—48no—
55C2×C22⋊D19D411yescharacteristic
56C22×Dic19—22no—
57D4×D19—24no—
58D4×D19—42no—
59C2×D76C2312yes—
60C2×C4×D19C2311yescharacteristic
61D8×C19—24no—
62D8×C19—22no—
63D8×C19D414yescomplemented
64C2×C8×C19—22no—
65C2×C8×C19C2311yescharacteristic
66C2×C8×C19C2311yescharacteristic
67C22⋊Dic19—22no—
68C22⋊Dic19—22no—
69C22⋊Dic19D411yescharacteristic
70#64525—24no—
71#64525—42no—
72(C2×D19)⋊C4—22no—
73(C2×D19)⋊C4D411yescharacteristic
74C4⋊Dic19C2312yes—
75Dic19⋊C4D411yescharacteristic
76C4×Dic19C2311yescharacteristic
77C2×C19⋊C8C2311yescharacteristic
78C2×C19⋊C8C2311yescharacteristic
79D152—22no—
80C8×D19—22no—
81C23×C19—22no—
82C23×C19—22no—
83C23×C19—44no—
84C23×C19—44no—
85C23×C19—82no—
86C23×C19C2×D411yescharacteristic
87C22×D19—22no—
88C22×D19—44no—
89C22×D19—44no—
90C22×D19—82no—
91C22×D19C2×D411yescharacteristic
92D4×C19—22no—
93D4×C19—22no—
94D4×C19—22no—
95D4×C19—44no—
96D4×C19C2×D414yescomplemented
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19C2×D411yescharacteristic
100C2×C4×C19C2411yescharacteristic
101C22⋊D19—44no—
102C22⋊D19—44no—
103C22⋊D19—44no—
104C22⋊D19—44no—
105C22⋊D19—82no—
106C22⋊D19D814yesdirect product factor
107C2×Dic19—22no—
108C2×Dic19—44no—
109C2×Dic19C2×D411yescharacteristic
110C2×Dic19C2×D411yescharacteristic
111C2×Dic19C2×D411yescharacteristic
112D76—22no—
113D76—22no—
114C4×D19—21no—
115C4×D19—21no—
116C8×C19—21no—
117C8×C19C2×D412yescomplemented
118C19⋊C8—21no—
119C19⋊C8—21no—
120D4×D8—191nomaximal, Sylow
121C22×C19—21no—
122C22×C19—21no—
123C22×C19—24no—
124C22×C19—42no—
125C22×C19—42no—
126C22×C19—42no—
127C22×C19—42no—
128C22×C19—42no—
129C22×C19—88no—
130C22×C19C2×D812yescomplemented
131C22×C19C22×D411yescharacteristic
132C2×D19—21no—
133C2×D19—21no—
134C2×D19—42no—
135C2×D19—42no—
136C2×D19—42no—
137C2×D19—88no—
138C2×D19C2×D812yescomplemented
139C4×C19—21no—
140C4×C19C22×D411yescharacteristic
141C4×C19H(5,𝔽2)11yescharacteristic
142Dic19—21no—
143Dic19—21no—
144Dic19—42no—
145Dic19C2×D812yescomplemented
146C22×D8—191no—
147C22×D8D1911yescharacteristic, complemented
148D42—192no—
149#493—191no—
150#466—191no—
151#466—191no—
152#459—192no—
153#447—192no—
154#447—192no—
155C4×D8—191no—
156C8×D4—191no—
157C2×C19—22no—
158C2×C19—44no—
159C2×C19—82no—
160C2×C19D4211yescharacteristic
161C2×C19C22×D811yescharacteristic
162C2×C19#57611yescharacteristic
163D19—22no—
164D19—82no—
165C22×D4—192no—
166C22×D4—382no—
167C22×D4C2×D1912yescomplemented
168C2×D8—24no—
169C2×D8—192no—
170C2×D8—192no—
171C2×D8—191no—
172C2×D8—384no—
173C2×D8C2×D1911yescharacteristic
174C2×D8C2×D1912yescomplemented
175C2×D8C2×D1911yescharacteristic, complemented
176C22×C8—191no—
177C22×C8C2×D1911yescharacteristic, complemented
178#127—192no—
179#121—192no—
180#121—192no—
181#121—382no—
182#120—382no—
183#120—382no—
184C4×D4—191no—
185C4×D4—192no—
186#107—191no—
187C4⋊C8—191no—
188#102—192no—
189#102—192no—
190#102—192no—
191C22⋊C8—191no—
192C22⋊C8—191no—
193C4×C8—191no—
194C19D4×D811yescharacteristic, complemented, Sylow
195C24—22no—
196C24—382no—
197C2×D4—24no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—191no—
201C2×D4—192no—
202C2×D4—382no—
203C2×D4—382no—
204C2×D4—382no—
205C2×D4—384no—
206C2×D4—382no—
207C2×D4—382no—
208C2×D4—762no—
209C2×D4—768no—
210C2×D4C22×D1912yes—
211C2×D4C22×D1912yes—
212C22×C4—191no—
213C22×C4—382no—
214C22×C4C22×D1911yescharacteristic
215D8—24no—
216D8—22no—
217D8—384no—
218D8—382no—
219D8—762no—
220D8C22⋊D1914yesdirect product factor
221C2×C8—22no—
222C2×C8—191no—
223C2×C8—191no—
224C2×C8—382no—
225C2×C8C22×D1911yescharacteristic
226C2×C8C22×D1911yescharacteristic
227C4⋊C4—191no—
228C4⋊C4—192no—
229C22⋊C4—191no—
230C22⋊C4—191no—
231C22⋊C4—382no—
232C22⋊C4—382no—
233C22⋊C4—382no—
234C42—191no—
235C23—22no—
236C23—22no—
237C23—44no—
238C23—44no—
239C23—82no—
240C23—191no—
241C23—382no—
242C23—764no—
243C23—764no—
244C23—1522no—
245C23D4×D1911yescharacteristic
246D4—22no—
247D4—22no—
248D4—22no—
249D4—44no—
250D4—194no—
251D4—382no—
252D4—382no—
253D4—764no—
254D4—764no—
255D4—764no—
256D4—764no—
257D4—1522no—
258D4C2×C22⋊D1914yescomplemented
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—191no—
262C2×C4—191no—
263C2×C4—191no—
264C2×C4—381no—
265C2×C4—381no—
266C2×C4—382no—
267C2×C4—764no—
268C2×C4D4×D1911yescharacteristic
269C2×C4C23×D1911yescharacteristic
270C8—21no—
271C8—381no—
272C8—381no—
273C8C2×C22⋊D1912yescomplemented
274C22—21no—
275C22—21no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—88no—
283C22—192no—
284C22—381no—
285C22—381no—
286C22—762no—
287C22—762no—
288C22—762no—
289C22—1528no—
290C22D8×D1912yescomplemented
291C22C2×D4×D1911yescharacteristic
292C4—21no—
293C4—192no—
294C4—381no—
295C4—381no—
296C4—762no—
297C4#1059743011yescharacteristic
298C4C22×C22⋊D1911yescharacteristic
299C2—22no—
300C2—44no—
301C2—82no—
302C2—382no—
303C2—1522no—
304C2D4×C22⋊D1911yescharacteristic
305C2C2×D8×D1911yescharacteristic
306C2#1192734511yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC22×D8×C19C2
socleC22×C19C22×D4
hypercenterC22×D8D19
hypocenterC19D4×D8
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D19C2semidirect
2. D4×C22⋊D19C2semidirect
3. #11926919C2semidirect
4. #11926780C2semidirect
5. #11926777C2semidirect
6. #11926737C2semidirect
7. #11926678C2semidirect
8. #11926676C2semidirect
9. D8×Dic19C2semidirect
10. C8×C22⋊D19C2semidirect
11. C22×D8×C19C2semidirect
12. C22×D4×C19C22semidirect
14. C2×D4×D19C22semidirect
17. C2×D8×C19C22semidirect
18. C2×D8×C19C22semidirect
19. C22×C8×C19C22semidirect
21. #10597386C22semidirect
23. #10597384C22semidirect
25. D4×Dic19C22semidirect
26. C2×#64525C22semidirect
27. C2×#64525C22semidirect
28. #10597376C22semidirect
31. C2×D152C22semidirect
32. C2×C8×D19C22semidirect
33. #10597289C22semidirect
34. #10597289C22semidirect
35. C22⋊(C19⋊C8)C22semidirect
36. #10597278C22semidirect
37. (C2×D19)⋊C8C22semidirect
38. #10597275C22semidirect
39. Dic19⋊C8C22semidirect
40. C8×Dic19C22semidirect
63. D8×C19D4semidirect
96. D4×C19C2×D4semidirect
106. C22⋊D19D8direct (N × H)
117. C8×C19C2×D4semidirect
130. C22×C19C2×D8semidirect
138. C2×D19C2×D8semidirect
145. Dic19C2×D8semidirect
147. C22×D8D19semidirect
167. C22×D4C2×D19semidirect
174. C2×D8C2×D19semidirect
175. C2×D8C2×D19semidirect
177. C22×C8C2×D19semidirect
194. C19D4×D8semidirect
220. D8C22⋊D19direct (N × H)
258. D4C2×C22⋊D19semidirect
273. C8C2×C22⋊D19semidirect
290. C22D8×D19semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D192
D4×C22⋊D192
#119269192
#119267802
#119267772
#119267372
#119266782
#119266762
D8×Dic192
C8×C22⋊D192
C22×D8×C192
D4×D819