Finite Group Databasebeta

← #34046039

Subgroups — #34046039

Order 19072.

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

normal subgroups only

This group has 230 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#23749490C211yesmaximal, 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×C4×Dic149C2211yescharacteristic
17#18011844—21no—
18#18011842—21no—
19#18011818—22no—
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—
38C22⋊Dic149—21no—
39C4×Dic149—21no—
40C4×Dic149—21no—
41C4×Dic149Q812yescomplemented
42C22×C4×C149—21no—
43C22×C4×C149C2311yescharacteristic
44M16×C149—21no—
45M16×C149Q812yescomplemented
46C2×C8×C149—21no—
47C4⋊C4×C149—21no—
48C4⋊C4×C149—21no—
49C4⋊C4×C149D411yescharacteristic
50C4⋊C4×C149D411yescharacteristic
51C22⋊C4×C149—21no—
52C42×C149—21no—
53Dic298—82no—
54C2×Dic149—22no—
55C2×Dic149—21no—
56C2×Dic149—21no—
57C2×Dic149—22no—
58C2×Dic149—41no—
59C2×Dic149—41no—
60C2×Dic149—42no—
61#11924746—22no—
62C23×C149C2×D411yescharacteristic
63C2×C4×C149—21no—
64C2×C4×C149—21no—
65C2×C4×C149—42no—
66C2×C4×C149—41no—
67C2×C4×C149C2×D411yescharacteristic
68C2×C4×C149C2×D411yescharacteristic
69C2×C4×C149C2×Q811yescharacteristic
70C2×C4×C149C2×Q811yescharacteristic
71C2×C4×C149C2×Q811yescharacteristic
72C2×C4×C149#4111yescharacteristic
73C8×C149—22no—
74C22×C149—21no—
75C22×C149—21no—
76C22×C149#12011yescharacteristic
77C22×C149C22⋊Q811yescharacteristic
78C22×C149C4⋊Q811yescharacteristic
79C4×C149—41no—
80C4×C149—41no—
81C4×C149—81no—
82C4×C149C22⋊Q811yescharacteristic
83C4×C149C22⋊Q811yescharacteristic
84C4×C149C4⋊Q811yescharacteristic
85C4×C149C4⋊Q811yescharacteristic
86Dic149—42no—
87Dic149—41no—
88Dic149—42no—
89Dic149—41no—
90C2×C149—21no—
91C2×C149—21no—
92C2×C149#39511yescharacteristic
93C2×C149#45411yescharacteristic
94C2×C149#45511yescharacteristic
95C149#206111yescharacteristic, complemented, Sylow
96#2061—1491nomaximal, Sylow
97#544—1491no—
98#428—1491no—
99#428D14911yescharacteristic
100#382—1491no—
101#343—1491no—
102#339—1491no—
103#339—1491no—
104C2×M16—1491no—
105C2×M16C2×D14911yescharacteristic
106C4⋊Q8—2981no—
107C4⋊Q8—2981no—
108#125—2981no—
109#125—2981no—
110C22⋊Q8—2982no—
111#117—1491no—
112#117C2×D14911yescharacteristic
113C2×C4⋊C4—1491no—
114C2×C4⋊C4C2×D14911yescharacteristic
115C2×C42—1491no—
116#107—21no—
117#107—2981no—
118#106—21no—
119#106—2981no—
120#95—2982no—
121C2×Q8—2982no—
122C22×C4—21no—
123C22×C4—2981no—
124C22×C4—1492no—
125C22×C4C22×D14911yescharacteristic
126M16—21no—
127M16—2981no—
128M16—1492no—
129M16Dic29812yescomplemented
130C2×C8—21no—
131C2×C8—2981no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2982no—
135C4⋊C4—2982no—
136C4⋊C4—2982no—
137C4⋊C4—2981no—
138C4⋊C4—2981no—
139C4⋊C4—1491no—
140C4⋊C4—1491no—
141C4⋊C4C22⋊D14911yescharacteristic
142C4⋊C4C22⋊D14911yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—2981no—
145C42—21no—
146C42—2981no—
147C42—2981no—
148C42—1492no—
149C23D4×D14911yescharacteristic
150Q8—11922no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—2981no—
156C2×C4—2981no—
157C2×C4—2982no—
158C2×C4—2982no—
159C2×C4—5961no—
160C2×C4—5961no—
161C2×C4—5962no—
162C2×C4D4×D14911yescharacteristic
163C2×C4C2×C22⋊D14911yescharacteristic
164C2×C4Q8×D14911yescharacteristic
165C2×C4Q8×D14911yescharacteristic
166C2×C4C2×Dic29811yescharacteristic
167C2×C4#1455873611yescharacteristic
168C8—22no—
169C8—2982no—
170C22—21no—
171C22—21no—
172C22#1801187911yescharacteristic
173C22#1801188911yescharacteristic
174C22#1801191011yescharacteristic
175C4—41no—
176C4—41no—
177C4—81no—
178C4—5962no—
179C4—5961no—
180C4—5962no—
181C4—5961no—
182C4#1801188911yescharacteristic
183C4#1801189011yescharacteristic
184C4#1801190911yescharacteristic
185C4#1801191011yescharacteristic
186C2—21no—
187C2—21no—
188C2#2374954511yescharacteristic
189C2#2374979611yescharacteristic
190C2#2374980111yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#428×C149C2
socleC22×C149#120
prime radicalC23×C149C2×D4
hypercenter#428D149
hypocenterC149#2061
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
41. C4×Dic149Q8semidirect
45. M16×C149Q8semidirect
95. C149#2061semidirect
129. M16Dic298semidirect

Maximal subgroups

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

subgroupindex
#237502532
#237496652
#237494902
#237493932
#237493862
#237493842
#428×C1492
#2061149