Finite Group Databasebeta

← #34043779

Subgroups — #34043779

Order 19072.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#23750280C211yesmaximal, characteristic, complemented
2#23749971C211yesmaximal, characteristic, complemented
3#23749817C211yesmaximal, characteristic, complemented
4#23749370C211yesmaximal, characteristic, complemented
5D4⋊#11924746C211yesmaximal, characteristic, complemented
6#23749352C211yesmaximal, characteristic, complemented
7#459×C149C211yesmaximal, characteristic, complemented
8C2×#14558736—21no—
9C2×#14558721—21no—
10#18011911C2211yescharacteristic
11#18011893—22no—
12#18011890—21no—
13#18011882—21no—
14C4×D596C2211yescharacteristic
15C4⋊C4×D149—21no—
16C4⋊#11924746C2211yescharacteristic
17#18011832—22no—
18#18011832—21no—
19C4×#11924746C2211yescharacteristic
20C2×D8×C149—21no—
21#127×C149C2211yescharacteristic
22C4×D4×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24#102×C149—21no—
25#14558736—42no—
26#14558736—42no—
27C2×Dic298—21no—
28C2×D596D411yescharacteristic
29C2×C22⋊D149—22no—
30C2×C4×D149—22no—
31C2×C4×D149—21no—
32#14558721—42no—
33C2×#11924746—21no—
34C2×#11924746—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149D412yes—
37C4⋊Dic149D411yescharacteristic
38#14558715—22no—
39C22⋊Dic149—22no—
40#14558713—21no—
41C2×D4×C149—21no—
42C2×D4×C149—21no—
43C2×D4×C149—21no—
44C2×D4×C149D411yescharacteristic
45C22×C4×C149—21no—
46D8×C149—42no—
47C2×C8×C149—21no—
48C4⋊C4×C149D411yescharacteristic
49C22⋊C4×C149—21no—
50C42×C149C2311yescharacteristic
51C22×D149—21no—
52Dic298—41no—
53Dic298—41no—
54D596—21no—
55D596D812yescomplemented
56C22⋊D149—44no—
57C2×Dic149—22no—
58C2×Dic149—21no—
59C4×D149—44no—
60C4×D149—41no—
61C4×D149—41no—
62#11924746—41no—
63#11924746—41no—
64C23×C149—21no—
65C23×C149—41no—
66D4×C149—21no—
67D4×C149—21no—
68D4×C149—42no—
69D4×C149—41no—
70D4×C149—41no—
71D4×C149—41no—
72D4×C149—41no—
73C2×C4×C149—21no—
74C2×C4×C149—41no—
75C2×C4×C149—41no—
76C2×C4×C149C2×D411yescharacteristic
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2×D411yescharacteristic
79C8×C149—41no—
80C22×C149—41no—
81C22×C149—41no—
82C22×C149—41no—
83C22×C149—81no—
84C22×C149—81no—
85C22×C149—81no—
86C22×C149#12011yescharacteristic
87C2×D149—22no—
88C2×D149—41no—
89C2×D149—41no—
90C4×C149—21no—
91C4×C149—41no—
92C4×C149C2×D811yescharacteristic
93C4×C149#13511yescharacteristic
94C4×C149AGL(1,ℤ/8)11yescharacteristic
95C4×C149AGL(1,ℤ/8)11yescharacteristic
96Dic149—42no—
97Dic149—41no—
98C2×C149—81no—
99C2×C149—161no—
100C2×C149#44711yescharacteristic
101C2×C149#44911yescharacteristic
102C2×C149#45411yescharacteristic
103D149—42no—
104C149#162511yescharacteristic, complemented, Sylow
105#1625—1491nomaximal, Sylow
106#547—1491no—
107#486—1491no—
108#459—1491no—
109#459D14911yescharacteristic, complemented
110#332—1491no—
111D4⋊C8—1491no—
112D4⋊C8—1491no—
113C2×#41—2981no—
114C2×D8—21no—
115C2×D8—2981no—
116C4⋊Q8—1491no—
117#127C2×D14911yescharacteristic
118#123—2982no—
119C22⋊Q8—2981no—
120#121—2981no—
121C4×D4—1491no—
122C4×D4C2×D14911yescharacteristic
123C2×C4⋊C4—2981no—
124C4⋊C8—1491no—
125C4⋊C8C2×D14911yescharacteristic
126#102—21no—
127#102—2981no—
128#102—2982no—
129C4×C8—1491no—
130#41—5962no—
131#41—5962no—
132C2×Q8—2981no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—2982no—
137C2×D4—1491no—
138C2×D4C22⋊D14911yescharacteristic
139C22×C4—21no—
140C22×C4—2982no—
141C22×C4—2981no—
142D8—42no—
143D8—5962no—
144C2×C8—21no—
145C2×C8—2981no—
146C2×C8—2981no—
147C4⋊C4—2982no—
148C4⋊C4—2981no—
149C4⋊C4—1491no—
150C4⋊C4—1492no—
151C4⋊C4C22⋊D14911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2982no—
154C22⋊C4—2981no—
155C42C22×D14911yescharacteristic
156C23—21no—
157C23—41no—
158C23—2981no—
159Q8—5961no—
160Q8—5961no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—2981no—
169D4—5964no—
170D4—1492no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—2981no—
175C2×C4—2982no—
176C2×C4—5964no—
177C2×C4—5961no—
178C2×C4—5961no—
179C2×C4D4×D14911yescharacteristic
180C2×C4D4×D14911yescharacteristic
181C2×C4C2×C22⋊D14911yescharacteristic
182C8—41no—
183C8—5961no—
184C8—5961no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—2982no—
192C22—5961no—
193C22—5961no—
194C22#1801187911yescharacteristic
195C4—21no—
196C4—41no—
197C4—5962no—
198C4—5961no—
199C4D8×D14911yescharacteristic
200C4#1801193111yescharacteristic
201C4#1801193511yescharacteristic
202C4#1801193711yescharacteristic
203C2—81no—
204C2—161no—
205C2—5962no—
206C2#2374975711yescharacteristic
207C2#2374976811yescharacteristic
208C2#2374979611yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#459×C149C2
socleC22×C149#120
hypercenter#459D149
hypocenterC149#1625
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23750280C2semidirect
2. #23749971C2semidirect
3. #23749817C2semidirect
4. #23749370C2semidirect
5. D4⋊#11924746C2semidirect
6. #23749352C2semidirect
7. #459×C149C2semidirect
55. D596D8semidirect
104. C149#1625semidirect
109. #459D149semidirect

Maximal subgroups

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

subgroupindex
#237502802
#237499712
#237498172
#237493702
D4⋊#119247462
#237493522
#459×C1492
#1625149