Finite Group Databasebeta

← #34046034

Subgroups — #34046034

Order 19072.

246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 73 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#23750253C211yesmaximal, characteristic
2#23749665C211yesmaximal, characteristic
3#23749494C211yesmaximal, characteristic
4#23749393C211yesmaximal, characteristic
5#23749386C211yesmaximal, characteristic
6#23749384C211yesmaximal, characteristic
7#428×C149C211yesmaximal, characteristic
8C2×#14558720C2211yescharacteristic
9#18011911—21no—
10#18011910—21no—
11#18011903—21no—
12#18011902—21no—
13#18011888—22no—
14#18011870C2211yescharacteristic
15C2×C4⋊Dic149C2211yescharacteristic
16C2×#14558715—22no—
17C2×C4×Dic149C2211yescharacteristic
18#18011844—21no—
19#18011842—21no—
20C2×M16×C149C2211yescharacteristic
21#117×C149C2211yescharacteristic
22C2×C4⋊C4×C149C2211yescharacteristic
23#107×C149—21no—
24#106×C149—21no—
25C2×Dic298—22no—
26C22×Dic149—21no—
27C22×Dic149D412yes—
28#14558720—21no—
29#14558720Q812yescomplemented
30C2×#11924746—21no—
31C4⋊Dic149—22no—
32C4⋊Dic149—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149D411yescharacteristic
35C4⋊Dic149D411yescharacteristic
36#14558715—22no—
37#14558715—22no—
38#14558715—44no—
39C22⋊Dic149—21no—
40C4×Dic149—21no—
41C4×Dic149—21no—
42C4×Dic149Q812yescomplemented
43C22×C4×C149—21no—
44C22×C4×C149C2311yescharacteristic
45M16×C149—21no—
46M16×C149Q812yescomplemented
47C2×C8×C149—21no—
48C4⋊C4×C149—21no—
49C4⋊C4×C149—21no—
50C4⋊C4×C149D411yescharacteristic
51C4⋊C4×C149D411yescharacteristic
52C22⋊C4×C149—21no—
53C42×C149—21no—
54Dic298—82no—
55C2×Dic149—22no—
56C2×Dic149—22no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—21no—
60C2×Dic149—21no—
61C2×Dic149—42no—
62#11924746—22no—
63C23×C149C2×D411yescharacteristic
64C2×C4×C149—21no—
65C2×C4×C149—21no—
66C2×C4×C149—42no—
67C2×C4×C149—41no—
68C2×C4×C149C2×D411yescharacteristic
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149C2×Q811yescharacteristic
71C2×C4×C149C2×Q811yescharacteristic
72C2×C4×C149C2×Q811yescharacteristic
73C2×C4×C149#4111yescharacteristic
74C8×C149—22no—
75C22×C149—21no—
76C22×C149—21no—
77C22×C149#12011yescharacteristic
78C22×C149C22⋊Q811yescharacteristic
79C22×C149C4⋊Q811yescharacteristic
80C4×C149—41no—
81C4×C149—41no—
82C4×C149—81no—
83C4×C149C22⋊Q811yescharacteristic
84C4×C149C22⋊Q811yescharacteristic
85C4×C149C4⋊Q811yescharacteristic
86C4×C149C4⋊Q811yescharacteristic
87Dic149—24no—
88Dic149—42no—
89Dic149—41no—
90Dic149—41no—
91C2×C149—21no—
92C2×C149—21no—
93C2×C149#39511yescharacteristic
94C2×C149#45311yescharacteristic
95C2×C149#45611yescharacteristic
96C149#206011yescharacteristic, complemented, Sylow
97#2060—1491nomaximal, Sylow
98#544—1491no—
99#428—1491no—
100#428D14911yescharacteristic
101#384—1491no—
102#343—1491no—
103#339—1491no—
104#339—1491no—
105C2×M16—1491no—
106C2×M16C2×D14911yescharacteristic
107C4⋊Q8—2981no—
108C4⋊Q8—2981no—
109#125—2981no—
110#125—2981no—
111C22⋊Q8—2982no—
112#117—1491no—
113#117C2×D14911yescharacteristic
114C2×C4⋊C4—2982no—
115C2×C4⋊C4—1491no—
116C2×C4⋊C4C2×D14911yescharacteristic
117C2×C42—1491no—
118#107—21no—
119#107—2981no—
120#106—21no—
121#106—2981no—
122C2×Q8—2982no—
123C22×C4—21no—
124C22×C4—2981no—
125C22×C4—1492no—
126C22×C4C22×D14911yescharacteristic
127M16—21no—
128M16—2981no—
129M16—1492no—
130M16Dic29812yescomplemented
131C2×C8—21no—
132C2×C8—2981no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—2982no—
136C4⋊C4—2982no—
137C4⋊C4—2982no—
138C4⋊C4—2981no—
139C4⋊C4—2981no—
140C4⋊C4—5964no—
141C4⋊C4—1491no—
142C4⋊C4—1491no—
143C4⋊C4C22⋊D14911yescharacteristic
144C4⋊C4C22⋊D14911yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—2981no—
147C42—21no—
148C42—2981no—
149C42—2981no—
150C42—1492no—
151C23D4×D14911yescharacteristic
152Q8—11922no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—2982no—
158C2×C4—2982no—
159C2×C4—2982no—
160C2×C4—2981no—
161C2×C4—2981no—
162C2×C4—2982no—
163C2×C4—5962no—
164C2×C4D4×D14911yescharacteristic
165C2×C4C2×C22⋊D14911yescharacteristic
166C2×C4Q8×D14911yescharacteristic
167C2×C4Q8×D14911yescharacteristic
168C2×C4C2×Dic29811yescharacteristic
169C2×C4#1455873611yescharacteristic
170C8—22no—
171C8—2982no—
172C22—21no—
173C22—21no—
174C22#1801187911yescharacteristic
175C22#1801188911yescharacteristic
176C22#1801191011yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—2984no—
181C4—5962no—
182C4—5961no—
183C4—5961no—
184C4#1801188911yescharacteristic
185C4#1801189011yescharacteristic
186C4#1801190911yescharacteristic
187C4#1801191011yescharacteristic
188C2—21no—
189C2—21no—
190C2#2374954511yescharacteristic
191C2#2374979111yescharacteristic
192C2#2374980611yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#428×C149C2
socleC22×C149#120
prime radicalC23×C149C2×D4
hypercenter#428D149
hypocenterC149#2060
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
29. #14558720Q8semidirect
42. C4×Dic149Q8semidirect
46. M16×C149Q8semidirect
96. C149#2060semidirect
130. M16Dic298semidirect

Maximal subgroups

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

subgroupindex
#237502532
#237496652
#237494942
#237493932
#237493862
#237493842
#428×C1492
#2060149