Finite Group Databasebeta

← #14574428

Subgroups — #14574428

Order 2432.

424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#11927055C212yesmaximal, complemented
2#11926886C212yesmaximal, complemented
3#11926869C212yesmaximal, complemented
4#11926785C211yesmaximal, characteristic, complemented
5#11926780C211yesmaximal, characteristic, complemented
6#11926773C212yesmaximal, complemented
7#11926708C212yesmaximal, complemented
8#11926691C212yesmaximal, complemented
9C2×C19×C22⋊C8C211yesmaximal, characteristic, complemented
10C23×C4×C19C2211yescharacteristic
11C2×#64541C2212yes—
12C22×C8×C19C2211yescharacteristic
13C22×C8×C19C2211yescharacteristic
14#10597399—22no—
15#10597376C2212yes—
16#10597376C2212yes—
17#10597375—22no—
18C4×C22⋊D19—22no—
19C4×C22⋊D19—22no—
20#10597372C2212yes—
21#10597370C2212yes—
22#10597370C2212yes—
23C2×Dic76C2211yescharacteristic, complemented
24C2×D152C2211yescharacteristic, complemented
25C2×#64516C2212yescomplemented
26C19×C22⋊C8C2212yes—
27C19×C22⋊C8C2212yes—
28#10597278C2212yescomplemented
29#10597278C2212yescomplemented
30#10597275C2211yescharacteristic, complemented
31#10597275C2211yescharacteristic, complemented
32#10597274C2212yescomplemented
33#10597273C2212yescomplemented
34#10597273C2212yescomplemented
35C24×C19D411yescharacteristic
36C22×C4×C19—41no—
37C22×C4×C19—41no—
38C22×C4×C19D411yescharacteristic
39C22×C4×C19D412yes—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2312yes—
42C2×C22⋊D19—22no—
43C2×C22⋊D19—22no—
44C2×C22⋊D19—22no—
45#64541—42no—
46#64541—42no—
47C2×D76C2312yes—
48C2×C4×D19—22no—
49C2×Dic38C2312yes—
50C2×C8×C19—41no—
51C2×C8×C19—41no—
52C2×C8×C19C2311yescharacteristic
53C2×C8×C19C2312yes—
54C2×C8×C19C2311yescharacteristic
55C22⋊Dic19—22no—
56C22⋊Dic19—22no—
57C22⋊Dic19—22no—
58(C2×D19)⋊C4—22no—
59(C2×D19)⋊C4—22no—
60C4⋊Dic19C2312yes—
61C4⋊Dic19C2312yes—
62Dic19⋊C4—22no—
63Dic19⋊C4—22no—
64C4×Dic19—22no—
65Dic76—41no—
66D152—41no—
67#64516—42no—
68C23×C19—22no—
69C23×C19—41no—
70C23×C19—41no—
71C23×C19C2×D412yes—
72C23×C19C2×D411yescharacteristic
73C22×D19—22no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—41no—
79C2×C4×C19—42no—
80C2×C4×C19C2×D412yes—
81C2×C4×C19C2×D411yescharacteristic
82C2×C4×C19C2411yescharacteristic
83C22⋊D19—44no—
84C22⋊D19—44no—
85C22⋊D19—44no—
86C2×Dic19—22no—
87C2×Dic19—22no—
88C2×Dic19—22no—
89D76—22no—
90D76—22no—
91C4×D19—44no—
92Dic38—22no—
93Dic38—22no—
94C8×C19—22no—
95C8×C19—21no—
96C8×C19—21no—
97#3191—191nomaximal, Sylow
98C22×C19—21no—
99C22×C19—21no—
100C22×C19—22no—
101C22×C19—22no—
102C22×C19—22no—
103C22×C19—44no—
104C22×C19#13512yes—
105C22×C19C22×D411yescharacteristic
106C2×D19—42no—
107C2×D19—42no—
108C2×D19—42no—
109C4×C19—22no—
110C4×C19—21no—
111C4×C19H(5,𝔽2)11yescharacteristic
112C4×C19H(5,𝔽2)11yescharacteristic
113Dic19—42no—
114Dic19—42no—
115Dic19—42no—
116#525—192no—
117#485—192no—
118#482—192no—
119#467—191no—
120#466—191no—
121#465—192no—
122#452—192no—
123#449—192no—
124C2×C22⋊C8D1911yescharacteristic, complemented
125C2×C19—22no—
126C2×C19—42no—
127C2×C19#53411yescharacteristic
128C2×C19C2×#13511yescharacteristic
129C2×C19#57511yescharacteristic
130D19—82no—
131C2×#41—192no—
132C23×C4C2×D1911yescharacteristic
133C2×Q16—191no—
134C2×SD16—192no—
135C2×D8—191no—
136C22×C8C2×D1911yescharacteristic
137C22×C8C2×D1911yescharacteristic
138#123—382no—
139C22⋊Q8—192no—
140C22⋊Q8—192no—
141#121—192no—
142#121—192no—
143#120—382no—
144C4×D4—382no—
145C4×D4—382no—
146#117—192no—
147#107—191no—
148#107—191no—
149#106—192no—
150#103—192no—
151#103—192no—
152#102—192no—
153#102—192no—
154C22⋊C8C2×D1912yes—
155C22⋊C8C2×D1912yes—
156C19#319111yescharacteristic, complemented, Sylow
157C24D7611yescharacteristic
158#41—762no—
159#41—762no—
160C2×Q8—192no—
161C2×D4—192no—
162C2×D4—382no—
163C2×D4—382no—
164C2×D4—382no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—382no—
168C22×C4D7611yescharacteristic
169C22×C4D7612yes—
170C22×C4C22×D1912yes—
171C22×C4C22×D1911yescharacteristic
172Q16—761no—
173SD16—762no—
174D8—761no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8C22×D1911yescharacteristic
178C2×C8C22×D1912yes—
179C2×C8C22×D1911yescharacteristic
180C4⋊C4—192no—
181C4⋊C4—192no—
182C4⋊C4—382no—
183C4⋊C4—382no—
184C22⋊C4—382no—
185C22⋊C4—382no—
186C22⋊C4—382no—
187C22⋊C4—382no—
188C22⋊C4—382no—
189C42—382no—
190C23—22no—
191C23—41no—
192C23—41no—
193C23—382no—
194C23C2×D7612yes—
195C23C2×D7611yescharacteristic
196Q8—382no—
197Q8—382no—
198D4—382no—
199D4—382no—
200D4—764no—
201D4—764no—
202D4—764no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—382no—
210C2×C4—382no—
211C2×C4—382no—
212C2×C4—764no—
213C2×C4C2×D7612yes—
214C2×C4C2×D7611yescharacteristic
215C2×C4C23×D1911yescharacteristic
216C8—21no—
217C8—22no—
218C8—21no—
219C22—21no—
220C22—21no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—44no—
225C22—762no—
226C22—762no—
227C22—762no—
228C22#1059735012yes—
229C22C22×D7611yescharacteristic
230C4—22no—
231C4—21no—
232C4—762no—
233C4—762no—
234C4—762no—
235C4#1059743011yescharacteristic
236C4#1059743011yescharacteristic
237C2—22no—
238C2—42no—
239C2—1522no—
240C2#1192710611yescharacteristic
241C2C2×#1059735011yescharacteristic
242C2#1192734411yescharacteristic
subgroupG/H
centerC22C22×D76
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×C22⋊C8C2
socleC22×C19C22×D4
hypercenterC2×C22⋊C8D19
hypocenterC19#3191
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #11927055C2semidirect
2. #11926886C2semidirect
3. #11926869C2semidirect
4. #11926785C2semidirect
5. #11926780C2semidirect
6. #11926773C2semidirect
7. #11926708C2semidirect
8. #11926691C2semidirect
9. C2×C19×C22⋊C8C2semidirect
23. C2×Dic76C22semidirect
24. C2×D152C22semidirect
25. C2×#64516C22semidirect
28. #10597278C22semidirect
29. #10597278C22semidirect
30. #10597275C22semidirect
31. #10597275C22semidirect
32. #10597274C22semidirect
33. #10597273C22semidirect
34. #10597273C22semidirect
124. C2×C22⋊C8D19semidirect
156. C19#3191semidirect

Maximal subgroups

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

subgroupindex
#119270552
#119268862
#119268692
#119267852
#119267802
#119267732
#119267082
#119266912
C2×C19×C22⋊C82
#319119