Finite Group Databasebeta

← #34043760

Subgroups — #34043760

Order 19072.

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

normal subgroups only

This group has 236 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#23750336C211yesmaximal, characteristic, complemented
2#23749822C211yesmaximal, characteristic, complemented
3#23749817C211yesmaximal, characteristic
4#23749374C211yesmaximal, characteristic, complemented
5#23749357C211yesmaximal, characteristic, complemented
6#23749354C211yesmaximal, characteristic, complemented
7#492×C149C211yesmaximal, characteristic, complemented
8C2×#14558724—21no—
9C2×#14558721—21no—
10#18011902—21no—
11#18011891—21no—
12#18011887—22no—
13C4×Dic298C2211yescharacteristic
14C4×D596C2211yescharacteristic
15#18011873—21no—
16C4⋊C4×D149—21no—
17C4⋊#11924746C2211yescharacteristic
18C4⋊#11924746C2211yescharacteristic
19#18011832—21no—
20#18011832—21no—
21C2×SD16×C149—22no—
22C4⋊Q8×C149C2211yescharacteristic
23#127×C149C2211yescharacteristic
24C4×C8×C149C2211yescharacteristic
25C2×Dic298D411yescharacteristic
26C2×D596D411yescharacteristic
27C2×C4×D149—22no—
28C2×C4×D149—21no—
29#14558724—42no—
30#14558721—42no—
31C2×#11924746—21no—
32C2×#11924746—21no—
33C4⋊Dic149—22no—
34C4⋊Dic149D411yescharacteristic
35C4⋊Dic149D411yescharacteristic
36#14558715—22no—
37#14558715—21no—
38#14558713—22no—
39#14558713—21no—
40C4×Dic149—21no—
41C2×Q8×C149D412yes—
42C2×D4×C149—21no—
43C2×D4×C149—21no—
44C2×D4×C149—21no—
45SD16×C149—44no—
46C2×C8×C149—21no—
47C4⋊C4×C149—21no—
48C4⋊C4×C149—21no—
49C42×C149C2311yescharacteristic
50C22×D149—21no—
51Dic298—21no—
52Dic298—21no—
53D596—21no—
54D596SD1612yescomplemented
55C2×Dic149—21no—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C4×D149—41no—
59C4×D149—41no—
60C4×D149—82no—
61#11924746—41no—
62#11924746—41no—
63C23×C149—41no—
64Q8×C149—42no—
65D4×C149—42no—
66D4×C149—41no—
67D4×C149—41no—
68D4×C149—41no—
69D4×C149—41no—
70C2×C4×C149—22no—
71C2×C4×C149C2×D411yescharacteristic
72C2×C4×C149C2×D411yescharacteristic
73C2×C4×C149C2×D411yescharacteristic
74C8×C149—22no—
75C22×C149—81no—
76C22×C149—81no—
77C22×C149—81no—
78C22×C149#12011yescharacteristic
79C2×D149—22no—
80C2×D149—41no—
81C2×D149—41no—
82C4×C149—21no—
83C4×C149—42no—
84C4×C149C2×SD1611yescharacteristic
85C4×C149#13511yescharacteristic
86C4×C149AGL(1,ℤ/8)11yescharacteristic
87C4×C149#13711yescharacteristic
88Dic149—41no—
89Dic149—41no—
90Dic149—41no—
91C2×C149—161no—
92C2×C149#44811yescharacteristic
93C2×C149#44911yescharacteristic
94C2×C149#45311yescharacteristic
95D149—42no—
96C149#162211yescharacteristic, complemented, Sylow
97#1622—1491nomaximal, Sylow
98#554—1491no—
99#492D14911yescharacteristic, complemented
100#460—1491no—
101#459—1491no—
102#333—1491no—
103Q8⋊C8—1491no—
104D4⋊C8—1491no—
105C2×SD16—22no—
106C2×SD16—2981no—
107C2×D8—2981no—
108C4⋊Q8C2×D14911yescharacteristic
109#127C2×D14911yescharacteristic
110#125—2981no—
111C22⋊Q8—2981no—
112C22⋊Q8—2982no—
113C4×Q8—1491no—
114C4×D4—2981no—
115C4×D4—1491no—
116C2×C4⋊C4—2981no—
117C4⋊C8—1491no—
118C4⋊C8—1491no—
119#102—2981no—
120#102—2981no—
121C4×C8C2×D14911yescharacteristic
122C2×Q8—1491no—
123C2×Q8C22⋊D14912yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—1491no—
128C22×C4—2982no—
129C22×C4—2981no—
130SD16—44no—
131SD16—5962no—
132D8—5962no—
133C2×C8—21no—
134C2×C8—2981no—
135C2×C8—2981no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2982no—
139C4⋊C4—2982no—
140C4⋊C4—2981no—
141C4⋊C4—1491no—
142C4⋊C4—1491no—
143C22⋊C4—2982no—
144C22⋊C4—2981no—
145C42—2981no—
146C42C22×D14911yescharacteristic
147C23—41no—
148C23—2981no—
149Q8—42no—
150Q8—2981no—
151Q8—2981no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—2981no—
158D4—1492no—
159C2×C4—22no—
160C2×C4—2981no—
161C2×C4—2981no—
162C2×C4—2981no—
163C2×C4—5961no—
164C2×C4—5961no—
165C2×C4—11922no—
166C2×C4D4×D14911yescharacteristic
167C2×C4D4×D14911yescharacteristic
168C2×C4C2×C22⋊D14911yescharacteristic
169C8—22no—
170C8—5961no—
171C8—5961no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—2982no—
176C22—5961no—
177C22—5961no—
178C22#1801187911yescharacteristic
179C4—21no—
180C4—42no—
181C4—5961no—
182C4—5961no—
183C4—5961no—
184C4SD16×D14911yescharacteristic
185C4#1801193211yescharacteristic
186C4#1801193811yescharacteristic
187C4#1801194011yescharacteristic
188C2—161no—
189C2—5962no—
190C2#2374976211yescharacteristic
191C2#2374976911yescharacteristic
192C2#2374979211yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#492×C149C2
socleC22×C149#120
prime radical#23749817C2
hypercenter#492D149
hypocenterC149#1622
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #23750336C2semidirect
2. #23749822C2semidirect
4. #23749374C2semidirect
5. #23749357C2semidirect
6. #23749354C2semidirect
7. #492×C149C2semidirect
54. D596SD16semidirect
96. C149#1622semidirect
99. #492D149semidirect

Maximal subgroups

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

subgroupindex
#237503362
#237498222
#237498172
#237493742
#237493572
#237493542
#492×C1492
#1622149