Finite Group Databasebeta

← #34043890

Subgroups — #34043890

Order 19072.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#23750297C211yesmaximal, characteristic
2#23749973C211yesmaximal, characteristic, complemented
3#23749827C211yesmaximal, characteristic, complemented
4#23749368C211yesmaximal, characteristic, complemented
5Q8⋊#11924746C211yesmaximal, characteristic, complemented
6#23749352C211yesmaximal, characteristic, complemented
7#475×C149C211yesmaximal, characteristic, complemented
8C2×#14558737—21no—
9C2×#14558723—21no—
10#18011908—21no—
11#18011908C2211yescharacteristic
12#18011886—21no—
13#18011886—22no—
14C4×D596—21no—
15C4×D596C2211yescharacteristic
16C4⋊#11924746C2211yescharacteristic
17#18011835—21no—
18#18011831—22no—
19C4×#11924746C2211yescharacteristic
20C4⋊Q8×C149C2211yescharacteristic
21C4×Q8×C149C2211yescharacteristic
22#106×C149—21no—
23C4⋊C8×C149C2211yescharacteristic
24#103×C149—21no—
25#14558737—42no—
26#14558737—42no—
27C2×D596—22no—
28C2×D596—22no—
29C2×D596—21no—
30C2×D596—21no—
31C2×D596D411yescharacteristic
32C2×D596D412yes—
33C2×C4×D149—22no—
34C2×C4×D149—21no—
35#14558723—42no—
36C2×#11924746—21no—
37C2×#11924746—21no—
38C4⋊Dic149D411yescharacteristic
39#14558713—22no—
40#14558713—21no—
41C2×Q8×C149—21no—
42C2×Q8×C149D411yescharacteristic
43C2×C8×C149—21no—
44C4⋊C4×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149—21no—
47C4⋊C4×C149D411yescharacteristic
48C42×C149—21no—
49C42×C149C2311yescharacteristic
50C22×D149—21no—
51C22×D149—22no—
52D596—21no—
53D596—21no—
54D596—42no—
55D596—44no—
56D596—41no—
57D596—41no—
58D596—41no—
59D596—41no—
60D596—82no—
61C2×Dic149—21no—
62C4×D149—44no—
63C4×D149—41no—
64C4×D149—41no—
65#11924746—41no—
66#11924746—41no—
67Q8×C149—21no—
68Q8×C149—41no—
69Q8×C149—41no—
70Q8×C149SD1612yescomplemented
71C2×C4×C149—21no—
72C2×C4×C149—21no—
73C2×C4×C149—41no—
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149C2×D411yescharacteristic
76C2×C4×C149C2×D411yescharacteristic
77C8×C149—41no—
78C22×C149#12011yescharacteristic
79C2×D149—41no—
80C2×D149—42no—
81C2×D149—42no—
82C2×D149—41no—
83C2×D149—42no—
84C2×D149—41no—
85C4×C149—22no—
86C4×C149—21no—
87C4×C149—41no—
88C4×C149—81no—
89C4×C149C2×SD1611yescharacteristic
90C4×C149#13511yescharacteristic
91C4×C149AGL(1,ℤ/8)11yescharacteristic
92C4×C149AGL(1,ℤ/8)11yescharacteristic
93Dic149—41no—
94C2×C149#44911yescharacteristic
95C2×C149#45011yescharacteristic
96C2×C149#45511yescharacteristic
97D149—81no—
98D149—82no—
99C149#164211yescharacteristic, complemented, Sylow
100#1642—1491nomaximal, Sylow
101#550—1491no—
102#486—1491no—
103#475D14911yescharacteristic, complemented
104#461—1491no—
105#331—1491no—
106Q8⋊C8—1491no—
107D4⋊C8—1491no—
108C2×#41—2981no—
109C2×SD16—2981no—
110C4⋊Q8C2×D14911yescharacteristic
111#127—2981no—
112#127—1491no—
113#121—2982no—
114#121—2981no—
115C4×Q8C2×D14911yescharacteristic
116C4×D4—2981no—
117C4×D4—1491no—
118#106—21no—
119C4⋊C8—1491no—
120C4⋊C8C2×D14911yescharacteristic
121#103—21no—
122#103—2981no—
123#102—2982no—
124C4×C8—1491no—
125#41—5962no—
126#41—5962no—
127C2×Q8—21no—
128C2×Q8C22⋊D14911yescharacteristic
129C2×D4—2982no—
130C2×D4—2982no—
131C2×D4—2981no—
132C2×D4—2981no—
133C2×D4—1491no—
134C2×D4—1492no—
135C22×C4—2982no—
136C22×C4—2981no—
137SD16—5962no—
138C2×C8—21no—
139C2×C8—2981no—
140C2×C8—2981no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—1491no—
145C4⋊C4C22⋊D14911yescharacteristic
146C22⋊C4—2982no—
147C22⋊C4—2981no—
148C42—21no—
149C42C22×D14911yescharacteristic
150C23—2981no—
151C23—2982no—
152Q8—21no—
153Q8—41no—
154Q8—41no—
155Q8#1455872312yescomplemented
156D4—2981no—
157D4—2981no—
158D4—5962no—
159D4—5964no—
160D4—5961no—
161D4—5961no—
162D4—5961no—
163D4—5961no—
164D4—11922no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—2981no—
169C2×C4—5964no—
170C2×C4—5961no—
171C2×C4—5961no—
172C2×C4D4×D14911yescharacteristic
173C2×C4D4×D14911yescharacteristic
174C2×C4C2×C22⋊D14911yescharacteristic
175C8—41no—
176C8—5961no—
177C8—5961no—
178C22—5961no—
179C22—5962no—
180C22—5962no—
181C22—5961no—
182C22—5962no—
183C22—5961no—
184C22#1801187911yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—81no—
189C4—5961no—
190C4C2×#1455872311yescharacteristic
191C4#1801193211yescharacteristic
192C4#1801193611yescharacteristic
193C4#1801193811yescharacteristic
194C2—11921no—
195C2—11922no—
196C2#2374976911yescharacteristic
197C2#2374977511yescharacteristic
198C2#2374980111yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#475×C149C2
socleC22×C149#120
prime radical#23750297C2
hypercenter#475D149
hypocenterC149#1642
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #23749973C2semidirect
3. #23749827C2semidirect
4. #23749368C2semidirect
5. Q8⋊#11924746C2semidirect
6. #23749352C2semidirect
7. #475×C149C2semidirect
70. Q8×C149SD16semidirect
99. C149#1642semidirect
103. #475D149semidirect
155. Q8#14558723semidirect

Maximal subgroups

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

subgroupindex
#237502972
#237499732
#237498272
#237493682
Q8⋊#119247462
#237493522
#475×C1492
#1642149