Finite Group Databasebeta

← #34043897

Subgroups — #34043897

Order 19072.

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

normal subgroups only

This group has 208 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#23750335C211yesmaximal, characteristic
2#23749977C211yesmaximal, characteristic, complemented
3#23749827C211yesmaximal, characteristic
4#23749373C211yesmaximal, characteristic, complemented
5Q8⋊#11924746C211yesmaximal, characteristic, complemented
6#23749352C211yesmaximal, characteristic
7#475×C149C211yesmaximal, characteristic, complemented
8C2×#14558723—21no—
9#18011911C2211yescharacteristic
10#18011903—21no—
11#18011889—22no—
12#18011887—21no—
13C4×D596—21no—
14C4×D596C2211yescharacteristic
15C4⋊C4×D149—21no—
16C4⋊#11924746C2211yescharacteristic
17#18011835—21no—
18#18011834—22no—
19C4×#11924746C2211yescharacteristic
20C4⋊Q8×C149C2211yescharacteristic
21C4×Q8×C149C2211yescharacteristic
22#106×C149—21no—
23C4⋊C8×C149C2211yescharacteristic
24#103×C149—21no—
25C2×Dic298D412yes—
26C2×D596D411yescharacteristic
27C2×C4×D149—22no—
28C2×C4×D149—21no—
29#14558723—42no—
30C2×#11924746—21no—
31C2×#11924746—21no—
32C4⋊Dic149—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149D411yescharacteristic
35#14558715—22no—
36#14558715—22no—
37#14558713—22no—
38#14558713—21no—
39C2×Q8×C149—21no—
40C2×Q8×C149D411yescharacteristic
41C2×C8×C149—21no—
42C4⋊C4×C149—21no—
43C4⋊C4×C149—21no—
44C4⋊C4×C149—21no—
45C4⋊C4×C149D411yescharacteristic
46C42×C149—21no—
47C42×C149C2311yescharacteristic
48C22×D149—21no—
49Dic298—42no—
50D596—21no—
51D596SD1612yes—
52C2×Dic149—22no—
53C2×Dic149—21no—
54C4×D149—41no—
55C4×D149—41no—
56C4×D149—82no—
57#11924746—41no—
58#11924746—41no—
59Q8×C149—21no—
60Q8×C149—21no—
61Q8×C149—41no—
62Q8×C149—41no—
63C2×C4×C149—21no—
64C2×C4×C149—21no—
65C2×C4×C149—41no—
66C2×C4×C149C2×D411yescharacteristic
67C2×C4×C149C2×D411yescharacteristic
68C2×C4×C149C2×D411yescharacteristic
69C8×C149—41no—
70C22×C149#12011yescharacteristic
71C2×D149—22no—
72C2×D149—41no—
73C2×D149—41no—
74C4×C149—21no—
75C4×C149—41no—
76C4×C149—41no—
77C4×C149—81no—
78C4×C149C2×SD1611yescharacteristic
79C4×C149#13511yescharacteristic
80C4×C149#13711yescharacteristic
81C4×C149#13711yescharacteristic
82Dic149—41no—
83Dic149—42no—
84C2×C149#44811yescharacteristic
85C2×C149#45211yescharacteristic
86C2×C149#45511yescharacteristic
87D149—42no—
88C149#164311yescharacteristic, complemented, Sylow
89#1643—1491nomaximal, Sylow
90#554—1491no—
91#487—1491no—
92#475D14911yescharacteristic, complemented
93#461—1491no—
94#333—1491no—
95Q8⋊C8—1491no—
96D4⋊C8—1491no—
97C2×SD16—2981no—
98C4⋊Q8—1491no—
99C4⋊Q8C2×D14911yescharacteristic
100#125—2981no—
101C22⋊Q8—2982no—
102C22⋊Q8—2981no—
103C4×Q8C2×D14911yescharacteristic
104C4×D4—2981no—
105C4×D4—1491no—
106C2×C4⋊C4—2981no—
107#106—21no—
108C4⋊C8—1491no—
109C4⋊C8C2×D14911yescharacteristic
110#103—21no—
111#103—2982no—
112#103—2981no—
113C4×C8—1491no—
114C2×Q8—21no—
115C2×Q8—1492no—
116C2×Q8C22⋊D14911yescharacteristic
117C2×D4—1491no—
118C22×C4—2982no—
119C22×C4—2981no—
120SD16—5962no—
121C2×C8—21no—
122C2×C8—2981no—
123C2×C8—2981no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—2982no—
128C4⋊C4—2982no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C4⋊C4—1491no—
132C4⋊C4C22⋊D14911yescharacteristic
133C22⋊C4—2982no—
134C22⋊C4—2981no—
135C42—21no—
136C42C22×D14911yescharacteristic
137C23—2981no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—5962no—
143D4—2981no—
144D4—1492no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—2981no—
149C2×C4—2982no—
150C2×C4—5961no—
151C2×C4—5961no—
152C2×C4—11922no—
153C2×C4D4×D14911yescharacteristic
154C2×C4D4×D14911yescharacteristic
155C2×C4C2×C22⋊D14911yescharacteristic
156C8—41no—
157C8—5961no—
158C8—5961no—
159C22—2982no—
160C22—5961no—
161C22—5961no—
162C22#1801187911yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—5961no—
168C4—5962no—
169C4SD16×D14911yescharacteristic
170C4#1801193111yescharacteristic
171C4#1801194011yescharacteristic
172C4#1801194211yescharacteristic
173C2—5962no—
174C2#2374976211yescharacteristic
175C2#2374978511yescharacteristic
176C2#2374980111yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#475×C149C2
socleC22×C149#120
prime radicalC2×D596D4
hypercenter#475D149
hypocenterC149#1643
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. #23749977C2semidirect
4. #23749373C2semidirect
5. Q8⋊#11924746C2semidirect
7. #475×C149C2semidirect
88. C149#1643semidirect
92. #475D149semidirect

Maximal subgroups

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

subgroupindex
#237503352
#237499772
#237498272
#237493732
Q8⋊#119247462
#237493522
#475×C1492
#1643149