Finite Group Databasebeta

← #34043713

Subgroups — #34043713

Order 19072.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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#23750187C211yesmaximal, characteristic
2#23749944C212yesmaximal, complemented
3#23749561C211yesmaximal, characteristic, complemented
4#23749360C212yesmaximal, complemented
5#323×C149C211yesmaximal, characteristic, complemented
6C22×C22⋊D149—21no—
7#18011895—22no—
8#18011885—21no—
9#18011885C2212yes—
10#18011881—22no—
11C2×C4⋊Dic149C2211yescharacteristic, complemented
12C2×#14558715—21no—
13C2×C22⋊Dic149—21no—
14#18011843—22no—
15#18011833—22no—
16#18011818C2211yescharacteristic, complemented
17C2×C22⋊C4×C149C2211yescharacteristic
18C22⋊C8×C149C2212yescomplemented
19C23×D149—21no—
20C2×D596—21no—
21C2×D596D412yes—
22C2×C22⋊D149—22no—
23C2×C22⋊D149—22no—
24C2×C22⋊D149—42no—
25C2×C22⋊D149—42no—
26C22×Dic149—21no—
27C22×Dic149—21no—
28C22×Dic149—21no—
29C4⋊Dic149—21no—
30C4⋊Dic149—22no—
31C4⋊Dic149D412yes—
32#14558715—42no—
33C22⋊Dic149—42no—
34#14558713—22no—
35#14558713—22no—
36C24×C149D411yescharacteristic
37C22×C4×C149D411yescharacteristic
38C22×C4×C149C2311yescharacteristic
39C2×C8×C149—22no—
40C22⋊C4×C149—22no—
41C22×D149—22no—
42C22×D149—42no—
43C22×D149—81no—
44C22×D149—81no—
45D596—42no—
46D596—81no—
47C22⋊D149—44no—
48C22⋊D149—42no—
49C22⋊D149—42no—
50C2×Dic149—22no—
51C2×Dic149—22no—
52C2×Dic149—41no—
53C2×Dic149—42no—
54C2×Dic149—41no—
55C2×Dic149—41no—
56C2×Dic149—41no—
57C2×Dic149—41no—
58C23×C149—21no—
59C23×C149—21no—
60C23×C149—41no—
61C23×C149—41no—
62C23×C149SD1612yes—
63C23×C149C2×D411yescharacteristic
64C2×C4×C149—21no—
65C2×C4×C149—41no—
66C2×C4×C149—41no—
67C2×C4×C149C2×D412yes—
68C8×C149—42no—
69C22×C149—21no—
70C22×C149—21no—
71C22×C149—22no—
72C22×C149—42no—
73C22×C149—41no—
74C22×C149—41no—
75C22×C149—81no—
76C22×C149#12011yescharacteristic
77C22×C149C2×SD1611yescharacteristic
78C22×C149AGL(1,ℤ/8)11yescharacteristic
79C2×D149—42no—
80C2×D149—42no—
81C2×D149—42no—
82C2×D149—84no—
83C4×C149—22no—
84C4×C149—41no—
85Dic149—42no—
86Dic149—42no—
87Dic149—81no—
88C2×C149—21no—
89C2×C149—21no—
90C2×C149—42no—
91C2×C149#45011yescharacteristic
92C2×C149#45311yescharacteristic
93C2×C149#45811yescharacteristic
94D149—82no—
95C149#161311yescharacteristic, complemented, Sylow
96#1613—1491nomaximal, Sylow
97#534—1491no—
98#481—1492no—
99#399—1491no—
100#327—1492no—
101#323D14911yescharacteristic, complemented
102C22×D4—2981no—
103#123—2982no—
104#121—2981no—
105#121—1492no—
106#120—2982no—
107C2×C4⋊C4—2981no—
108C2×C4⋊C4—1491no—
109C2×C22⋊C4—2981no—
110C2×C22⋊C4C2×D14911yescharacteristic
111#106—2982no—
112#102—2982no—
113C22⋊C8C2×D14912yescomplemented
114#95—1491no—
115C24—2981no—
116C24D59611yescharacteristic
117C2×D4—2981no—
118C2×D4—2982no—
119C2×D4—2982no—
120C2×D4—5962no—
121C2×D4—5962no—
122C2×D4—1492no—
123C22×C4—2981no—
124C22×C4—2981no—
125C22×C4—2981no—
126C22×C4D59611yescharacteristic
127C22×C4C22×D14911yescharacteristic
128C2×C8—22no—
129C4⋊C4—2981no—
130C4⋊C4—2982no—
131C4⋊C4—5962no—
132C4⋊C4—1492no—
133C22⋊C4—22no—
134C22⋊C4—2982no—
135C22⋊C4—2982no—
136C22⋊C4—5962no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—2982no—
142C23—5962no—
143C23—11921no—
144C23—11921no—
145C23#1455872512yes—
146C23C2×D59611yescharacteristic
147D4—5962no—
148D4—5964no—
149D4—5962no—
150D4—5962no—
151D4—11921no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—2982no—
156C2×C4—2982no—
157C2×C4—5961no—
158C2×C4—5962no—
159C2×C4—5961no—
160C2×C4—5961no—
161C2×C4—5961no—
162C2×C4—5961no—
163C2×C4D4×D14912yes—
164C8—42no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—5962no—
173C22—5962no—
174C22—5962no—
175C22—11924no—
176C22#1801188111yescharacteristic
177C22C2×#1455872511yescharacteristic
178C22#1801193911yescharacteristic
179C4—22no—
180C4—41no—
181C4—5962no—
182C4—5962no—
183C4—11921no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—11922no—
188C2#2374977811yescharacteristic
189C2#2374979511yescharacteristic
190C2#2374981611yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#323×C149C2
socleC22×C149#120
prime radical#23750187C2
hypercenter#323D149
hypocenterC149#1613
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #23749944C2semidirect
3. #23749561C2semidirect
4. #23749360C2semidirect
5. #323×C149C2semidirect
11. C2×C4⋊Dic149C22semidirect
16. #18011818C22semidirect
18. C22⋊C8×C149C22semidirect
95. C149#1613semidirect
101. #323D149semidirect
113. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501872
#237499442
#237495612
#237493602
#323×C1492
#1613149