Finite Group Databasebeta

← #34043749

Subgroups — #34043749

Order 19072.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#23750360C211yesmaximal, characteristic, complemented
2#23750001C211yesmaximal, characteristic
3#23749822C211yesmaximal, characteristic, complemented
4#23749368C211yesmaximal, characteristic, complemented
5Q8⋊#11924746C211yesmaximal, characteristic, complemented
6#23749355C211yesmaximal, characteristic, complemented
7#460×C149C211yesmaximal, characteristic, complemented
8C2×#14558724—21no—
9C2×#14558721—22no—
10#18011908C2211yescharacteristic
11#18011900—21no—
12#18011899—21no—
13#18011896—22no—
14C4×Dic298C2211yescharacteristic
15C4×D596—21no—
16#18011873—21no—
17C4⋊#11924746C2211yescharacteristic
18#18011832—21no—
19C4×#11924746C2211yescharacteristic
20C2×SD16×C149—21no—
21#127×C149C2211yescharacteristic
22C4×Q8×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24#102×C149—21no—
25C2×Dic298D411yescharacteristic
26C2×D596—21no—
27C2×D596—21no—
28C2×D596D412yes—
29C2×C4×D149—22no—
30#14558724—42no—
31#14558721—44no—
32C2×#11924746—21no—
33C2×#11924746—21no—
34C4⋊Dic149D411yescharacteristic
35#14558715—21no—
36#14558713—22no—
37#14558713—22no—
38#14558713—22no—
39C4×Dic149—21no—
40C2×Q8×C149D411yescharacteristic
41C2×D4×C149—21no—
42C2×D4×C149—21no—
43C2×D4×C149—21no—
44SD16×C149—42no—
45C2×C8×C149—21no—
46C4⋊C4×C149—21no—
47C4⋊C4×C149D411yescharacteristic
48C42×C149—21no—
49C42×C149C2311yescharacteristic
50C22×D149—22no—
51Dic298—21no—
52Dic298—21no—
53D596—42no—
54D596—41no—
55D596—41no—
56D596—41no—
57D596—41no—
58C2×Dic149—21no—
59C2×Dic149—21no—
60C4×D149—82no—
61#11924746—22no—
62#11924746—41no—
63C23×C149—41no—
64Q8×C149—21no—
65Q8×C149—21no—
66D4×C149—42no—
67D4×C149—41no—
68D4×C149—41no—
69D4×C149—41no—
70D4×C149—41no—
71C2×C4×C149—21no—
72C2×C4×C149—21no—
73C2×C4×C149C2×D411yescharacteristic
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149C2×D411yescharacteristic
76C8×C149—41no—
77C22×C149—81no—
78C22×C149—81no—
79C22×C149—81no—
80C22×C149#12011yescharacteristic
81C2×D149—42no—
82C2×D149—42no—
83C2×D149—42no—
84C4×C149—21no—
85C4×C149—41no—
86C4×C149—41no—
87C4×C149#13511yescharacteristic
88C4×C149#13511yescharacteristic
89C4×C149AGL(1,ℤ/8)11yescharacteristic
90C4×C149AGL(1,ℤ/8)11yescharacteristic
91Dic149—41no—
92Dic149—41no—
93C2×C149—161no—
94C2×C149#44911yescharacteristic
95C2×C149#44911yescharacteristic
96C2×C149#45311yescharacteristic
97D149—82no—
98C149#162011yescharacteristic, complemented, Sylow
99#1620—1491nomaximal, Sylow
100#559—1491no—
101#493—1491no—
102#460—1491no—
103#460D14911yescharacteristic, complemented
104#331—1491no—
105Q8⋊C8—1491no—
106Q8⋊C8—1491no—
107C2×SD16—21no—
108C2×SD16—2981no—
109C2×D8—2982no—
110#127—1491no—
111#127C2×D14911yescharacteristic
112#124—2981no—
113#124—2981no—
114#123—2982no—
115C4×Q8—1491no—
116C4×Q8C2×D14911yescharacteristic
117C4×D4—2981no—
118C4×D4—2981no—
119C4⋊C8—1491no—
120C4⋊C8C2×D14911yescharacteristic
121#102—21no—
122#102—2981no—
123C4×C8—1491no—
124C2×Q8—1491no—
125C2×Q8C22⋊D14911yescharacteristic
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—2981no—
130C2×D4—2981no—
131C2×D4—1492no—
132C22×C4—2982no—
133SD16—42no—
134SD16—5962no—
135D8—5964no—
136C2×C8—21no—
137C2×C8—2981no—
138C2×C8—2981no—
139C4⋊C4—21no—
140C4⋊C4—2981no—
141C4⋊C4—1491no—
142C4⋊C4C22⋊D14911yescharacteristic
143C22⋊C4—2982no—
144C22⋊C4—2982no—
145C22⋊C4—2982no—
146C42—21no—
147C42—2981no—
148C42C22×D14911yescharacteristic
149C23—41no—
150C23—2982no—
151Q8—21no—
152Q8—21no—
153Q8—2981no—
154Q8—2981no—
155D4—42no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—5962no—
161D4—5961no—
162D4—5961no—
163D4—5961no—
164D4—5961no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—2981no—
168C2×C4—2981no—
169C2×C4—11922no—
170C2×C4D4×D14911yescharacteristic
171C2×C4D4×D14911yescharacteristic
172C2×C4C2×C22⋊D14911yescharacteristic
173C8—41no—
174C8—2982no—
175C8—5961no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—5962no—
180C22—5962no—
181C22—5962no—
182C22#1801187911yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—5961no—
187C4—5961no—
188C4#1801193111yescharacteristic
189C4#1801193211yescharacteristic
190C4#1801193711yescharacteristic
191C4#1801193811yescharacteristic
192C2—161no—
193C2—11922no—
194C2#2374976811yescharacteristic
195C2#2374976911yescharacteristic
196C2#2374979111yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#460×C149C2
socleC22×C149#120
prime radical#23750001C2
hypercenter#460D149
hypocenterC149#1620
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #23750360C2semidirect
3. #23749822C2semidirect
4. #23749368C2semidirect
5. Q8⋊#11924746C2semidirect
6. #23749355C2semidirect
7. #460×C149C2semidirect
98. C149#1620semidirect
103. #460D149semidirect

Maximal subgroups

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

subgroupindex
#237503602
#237500012
#237498222
#237493682
Q8⋊#119247462
#237493552
#460×C1492
#1620149