Finite Group Databasebeta

← #34043850

Subgroups — #34043850

Order 19072.

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

normal subgroups only

This group has 188 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#23750350C211yesmaximal, characteristic
2#23749977C211yesmaximal, characteristic
3#23749921C211yesmaximal, characteristic
4#23749921C211yesmaximal, characteristic
5#23749355C211yesmaximal, characteristic
6#23749355C211yesmaximal, characteristic
7#332×C149C211yesmaximal, characteristic
8#18011911C2211yescharacteristic
9#18011909—21no—
10#18011902—21no—
11#18011901—22no—
12Q8×Dic149—21no—
13C4×Dic298C2211yescharacteristic
14C4×Dic298C2211yescharacteristic
15#18011876—21no—
16#18011845—21no—
17#18011845—21no—
18#18011836—21no—
19#18011836—21no—
20#18011834—22no—
21C4×#11924746C2211yescharacteristic
22C4⋊Q8×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4⋊C8×C149C2211yescharacteristic
25C2×Dic298—21no—
26C2×Dic298D411yescharacteristic
27C2×Dic298D411yescharacteristic
28C2×#11924746—21no—
29C4⋊Dic149—22no—
30C4⋊Dic149—21no—
31C4⋊Dic149—21no—
32C4⋊Dic149D411yescharacteristic
33C4⋊Dic149D411yescharacteristic
34#14558715—22no—
35#14558715—22no—
36#14558715—21no—
37#14558715—21no—
38C4×Dic149—22no—
39C4×Dic149—21no—
40C4×Dic149—21no—
41C2×Q8×C149—21no—
42C2×C8×C149—21no—
43C2×C8×C149—21no—
44C4⋊C4×C149—21no—
45C4⋊C4×C149D412yes—
46C42×C149C2311yescharacteristic
47Dic298—21no—
48Dic298—21no—
49Dic298—21no—
50Dic298—42no—
51Dic298Q1612yes—
52C2×Dic149—21no—
53C2×Dic149—21no—
54C2×Dic149—21no—
55C2×Dic149—21no—
56C2×Dic149—41no—
57#11924746—41no—
58Q8×C149—41no—
59Q8×C149—41no—
60C2×C4×C149—22no—
61C2×C4×C149C2×D411yescharacteristic
62C2×C4×C149C2×D411yescharacteristic
63C2×C4×C149C2×D411yescharacteristic
64C8×C149—41no—
65C8×C149—41no—
66C22×C149#12011yescharacteristic
67C4×C149—21no—
68C4×C149—42no—
69C4×C149C2×Q1611yescharacteristic
70C4×C149#13511yescharacteristic
71C4×C149#13711yescharacteristic
72C4×C149#13711yescharacteristic
73Dic149—22no—
74Dic149—41no—
75Dic149—41no—
76Dic149—41no—
77Dic149—81no—
78C2×C149#45111yescharacteristic
79C2×C149#45211yescharacteristic
80C2×C149#45411yescharacteristic
81C149#163611yescharacteristic, complemented, Sylow
82#1636—1491nomaximal, Sylow
83#557—1491no—
84#487—1491no—
85#477—1491no—
86#477—1491no—
87#332D14911yescharacteristic
88Q8⋊C8—1491no—
89Q8⋊C8—1491no—
90C4⋊Q8—2981no—
91C4⋊Q8—1491no—
92C4⋊Q8C2×D14911yescharacteristic
93#125—2981no—
94#125—2982no—
95C4×Q8—2981no—
96C4×Q8—2981no—
97C4×Q8—1491no—
98C4×Q8—1491no—
99#107—2981no—
100#107—2981no—
101C4⋊C8C2×D14911yescharacteristic
102C4⋊C8C2×D14911yescharacteristic
103#103—2981no—
104#103—2981no—
105#103—2982no—
106C4×C8—1491no—
107C2×Q8—21no—
108C2×Q8—2981no—
109C2×Q8—1491no—
110C2×Q8—1491no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—2981no—
114C4⋊C4—21no—
115C4⋊C4—2982no—
116C4⋊C4—2982no—
117C4⋊C4—2982no—
118C4⋊C4—2981no—
119C4⋊C4—2981no—
120C4⋊C4—2981no—
121C4⋊C4—2981no—
122C4⋊C4—1491no—
123C4⋊C4—1491no—
124C4⋊C4D59612yes—
125C42—2982no—
126C42—2981no—
127C42—2981no—
128C42C22×D14911yescharacteristic
129Q8—41no—
130Q8—41no—
131Q8—2981no—
132Q8—2981no—
133Q8—2981no—
134Q8—5962no—
135Q8—1492no—
136C2×C4—22no—
137C2×C4—2981no—
138C2×C4—2981no—
139C2×C4—2981no—
140C2×C4—2981no—
141C2×C4—5961no—
142C2×C4D4×D14911yescharacteristic
143C2×C4D4×D14911yescharacteristic
144C2×C4C2×D59611yescharacteristic
145C8—41no—
146C8—41no—
147C8—5961no—
148C22#1801188111yescharacteristic
149C4—21no—
150C4—42no—
151C4—2982no—
152C4—5961no—
153C4—5961no—
154C4—5961no—
155C4—11921no—
156C4Q16×D14911yescharacteristic
157C4#1801193011yescharacteristic
158C4#1801194011yescharacteristic
159C4#1801194011yescharacteristic
160C2#2374978211yescharacteristic
161C2#2374978811yescharacteristic
162C2#2374980011yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#332×C149C2
socle, prime radicalC22×C149#120
hypercenter#332D149
hypocenterC149#1636
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
81. C149#1636semidirect

Maximal subgroups

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

subgroupindex
#237503502
#237499772
#237499212
#237493552
#332×C1492
#1636149