Finite Group Databasebeta

← #34046045

Subgroups — #34046045

Order 19072.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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#23750251C211yesmaximal, characteristic
2#23749500C212yesmaximal
3#23749497C211yesmaximal, characteristic
4#23749391C212yesmaximal
5#342×C149C211yesmaximal, characteristic
6C23×Dic149C2211yescharacteristic
7#18011890—21no—
8#18011890—21no—
9#18011888—22no—
10#18011888—22no—
11C2×C4⋊Dic149—22no—
12C2×#14558715—21no—
13C2×C22⋊Dic149C2211yescharacteristic
14C2×C22⋊Dic149C2212yes—
15#18011818—21no—
16#18011818—22no—
17C2×C22⋊C4×C149C2211yescharacteristic
18C2×C22⋊C4×C149C2212yes—
19C2×Dic298—21no—
20C2×Dic298—21no—
21C22×Dic149—21no—
22C22×Dic149—22no—
23C22×Dic149—21no—
24C22×Dic149—42no—
25C22×Dic149D412yes—
26C22×Dic149D412yes—
27C4⋊Dic149—21no—
28C4⋊Dic149—21no—
29C4⋊Dic149—44no—
30#14558715—22no—
31#14558715—22no—
32#14558715—42no—
33C22⋊Dic149—22no—
34C22⋊Dic149—22no—
35C22⋊Dic149—21no—
36C22⋊Dic149Q812yescomplemented
37C24×C149C2311yescharacteristic
38C22×C4×C149—22no—
39C22×C4×C149D411yescharacteristic
40C22×C4×C149D411yescharacteristic
41C22⋊C4×C149—22no—
42C22⋊C4×C149—22no—
43C22⋊C4×C149Q814yescomplemented
44Dic298—81no—
45Dic298—81no—
46C2×Dic149—22no—
47C2×Dic149—24no—
48C2×Dic149—22no—
49C2×Dic149—22no—
50C2×Dic149—22no—
51C2×Dic149—41no—
52C2×Dic149—41no—
53C2×Dic149—42no—
54C2×Dic149—41no—
55C2×Dic149—41no—
56C2×Dic149—42no—
57C2×Dic149—42no—
58C23×C149—41no—
59C23×C149—41no—
60C23×C149C2×D412yes—
61C23×C149C2×D411yescharacteristic
62C23×C149C2×Q811yescharacteristic
63C23×C149C2×Q812yes—
64C23×C149#4111yescharacteristic
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149—24no—
68C2×C4×C149—42no—
69C2×C4×C149—42no—
70C2×C4×C149—41no—
71C2×C4×C149—41no—
72C22×C149—22no—
73C22×C149—21no—
74C22×C149—22no—
75C22×C149—21no—
76C22×C149—41no—
77C22×C149—42no—
78C22×C149—41no—
79C22×C149#12011yescharacteristic
80C22×C149C22⋊Q812yes—
81C22×C149C22⋊Q811yescharacteristic
82C22×C149C4⋊Q812yes—
83C22×C149C4⋊Q811yescharacteristic
84C4×C149—44no—
85C4×C149—41no—
86C4×C149—41no—
87Dic149—42no—
88Dic149—42no—
89Dic149—42no—
90Dic149—42no—
91C2×C149—21no—
92C2×C149—22no—
93C2×C149—22no—
94C2×C149—21no—
95C2×C149#39511yescharacteristic
96C2×C149B(4,𝔽2)11yescharacteristic
97C2×C149#45811yescharacteristic
98C149#206211yescharacteristic, complemented, Sylow
99#2062—1491nomaximal, Sylow
100#543—1491no—
101#385—1491no—
102#385—1492no—
103#342—1492no—
104#342D14911yescharacteristic
105C23×C4—1491no—
106C22⋊Q8—2982no—
107C22⋊Q8—2982no—
108C22⋊Q8—2981no—
109C22⋊Q8—2981no—
110C2×C4⋊C4—2982no—
111C2×C4⋊C4—2981no—
112C2×C22⋊C4—1492no—
113C2×C22⋊C4—1491no—
114C2×C22⋊C4C2×D14911yescharacteristic
115C2×C22⋊C4C2×D14912yes—
116#95—2982no—
117#95—2981no—
118C24C22×D14911yescharacteristic
119C2×Q8—2981no—
120C2×Q8—2981no—
121C22×C4—22no—
122C22×C4—2982no—
123C22×C4—2981no—
124C22×C4—2981no—
125C22×C4—5962no—
126C22×C4—1492no—
127C22×C4—1492no—
128C22×C4D59611yescharacteristic
129C22×C4D59611yescharacteristic
130C4⋊C4—2982no—
131C4⋊C4—2982no—
132C4⋊C4—2981no—
133C4⋊C4—2981no—
134C4⋊C4—5962no—
135C4⋊C4—5964no—
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—2982no—
139C22⋊C4—2982no—
140C22⋊C4—2981no—
141C22⋊C4—1492no—
142C22⋊C4Dic29814yescomplemented
143C23—41no—
144C23—41no—
145C23D4×D14912yes—
146C23C2×D59611yescharacteristic
147C23Q8×D14911yescharacteristic
148C23C2×Dic29812yes—
149C23#1455873511yescharacteristic
150Q8—11921no—
151Q8—11921no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—24no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—2984no—
160C2×C4—2982no—
161C2×C4—2982no—
162C2×C4—2982no—
163C2×C4—2982no—
164C2×C4—5961no—
165C2×C4—5961no—
166C2×C4—5962no—
167C2×C4—5961no—
168C2×C4—5961no—
169C2×C4—5962no—
170C2×C4—5962no—
171C22—22no—
172C22—21no—
173C22—22no—
174C22—21no—
175C22—41no—
176C22—42no—
177C22—41no—
178C22#1801188111yescharacteristic
179C22#1801188812yes—
180C22#1801189111yescharacteristic
181C22#1801191012yes—
182C22#1801191111yescharacteristic
183C4—44no—
184C4—41no—
185C4—41no—
186C4—5962no—
187C4—5962no—
188C4—5962no—
189C4—5962no—
190C2—22no—
191C2—21no—
192C2—22no—
193C2—21no—
194C2#2374954611yescharacteristic
195C2#2374981311yescharacteristic
196C2#2374981611yescharacteristic
subgroupG/H
centerC22#18011881
commutator, prime radical, cosocleC24×C149C23
FrattiniC24C22×D149
Fitting#342×C149C2
socleC22×C149#120
hypercenter#342D149
hypocenterC149#2062
LCSG ▷ C24×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
36. C22⋊Dic149Q8semidirect
43. C22⋊C4×C149Q8semidirect
98. C149#2062semidirect
142. C22⋊C4Dic298semidirect

Maximal subgroups

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

subgroupindex
#237502512
#237495002
#237494972
#237493912
#342×C1492
#2062149