Finite Group Databasebeta

← #34043859

Subgroups — #34043859

Order 19072.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic298C211yesmaximal, characteristic
2#23749976C211yesmaximal, characteristic, complemented
3#23749921C211yesmaximal, characteristic, complemented
4#23749915C211yesmaximal, characteristic
5#23749372C211yesmaximal, characteristic, complemented
6#23749357C211yesmaximal, characteristic, complemented
7D4⋊C8×C149C211yesmaximal, characteristic
8C22×Dic298—21no—
9#18011911C2211yescharacteristic
10#18011911C2211yescharacteristic
11#18011910—21no—
12#18011890—21no—
13#18011888—22no—
14C4×Dic298C2211yescharacteristic
15D4×Dic149—21no—
16#18011845—21no—
17#18011842—21no—
18C4⋊#11924746C2211yescharacteristic
19#18011836—22no—
20#18011836—21no—
21#18011832—21no—
22C4×D4×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4×C8×C149C2211yescharacteristic
25C2×Dic298—22no—
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×Dic298—42no—
29C2×Dic298—42no—
30C2×Dic298D411yescharacteristic
31C22×Dic149—22no—
32C2×#11924746—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149D412yes—
37C4⋊Dic149D411yescharacteristic
38#14558715—22no—
39#14558715—21no—
40C22⋊Dic149—22no—
41C4×Dic149—21no—
42C2×D4×C149D411yescharacteristic
43C22×C4×C149—21no—
44C2×C8×C149—21no—
45C2×C8×C149—21no—
46C4⋊C4×C149D411yescharacteristic
47C22⋊C4×C149—21no—
48C42×C149C2311yescharacteristic
49Dic298—21no—
50Dic298—44no—
51Dic298—41no—
52Dic298—41no—
53Dic298—42no—
54Dic298SD1612yes—
55C2×Dic149—21no—
56C2×Dic149—22no—
57C2×Dic149—21no—
58C2×Dic149—44no—
59C2×Dic149—41no—
60#11924746—41no—
61C23×C149—21no—
62D4×C149—21no—
63D4×C149Q1612yes—
64C2×C4×C149—21no—
65C2×C4×C149—41no—
66C2×C4×C149—41no—
67C2×C4×C149C2×D411yescharacteristic
68C2×C4×C149C2×D411yescharacteristic
69C2×C4×C149C2×D411yescharacteristic
70C8×C149—41no—
71C8×C149—41no—
72C22×C149—22no—
73C22×C149—41no—
74C22×C149—41no—
75C22×C149#12011yescharacteristic
76C4×C149—21no—
77C4×C149—41no—
78C4×C149C2×SD1611yescharacteristic
79C4×C149C2×Q1611yescharacteristic
80C4×C149AGL(1,ℤ/8)11yescharacteristic
81C4×C149#13711yescharacteristic
82Dic149—22no—
83Dic149—42no—
84Dic149—41no—
85Dic149—81no—
86C2×C149—42no—
87C2×C149#45011yescharacteristic
88C2×C149#45111yescharacteristic
89C2×C149#45411yescharacteristic
90C149#163711yescharacteristic, complemented, Sylow
91#1637—1491nomaximal, Sylow
92D4×Q8—1491no—
93#487—1491no—
94#477—1491no—
95#476—1491no—
96#332—1491no—
97Q8⋊C8—1491no—
98D4⋊C8D14911yescharacteristic
99C22×Q8—2981no—
100C4⋊Q8—2981no—
101C4⋊Q8—1491no—
102C4⋊Q8—1491no—
103C22⋊Q8—2982no—
104C22⋊Q8—2981no—
105C4×Q8—1491no—
106C4×D4—2981no—
107C4×D4C2×D14911yescharacteristic
108#107—2981no—
109#106—2981no—
110C4⋊C8—1491no—
111C4⋊C8C2×D14911yescharacteristic
112#103—2981no—
113#103—2982no—
114#102—2981no—
115C4×C8C2×D14911yescharacteristic
116C2×Q8—2982no—
117C2×Q8—2981no—
118C2×Q8—2981no—
119C2×Q8—5962no—
120C2×Q8—5962no—
121C2×Q8—1491no—
122C2×D4D59611yescharacteristic
123C22×C4—21no—
124C22×C4—2982no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—2981no—
128C4⋊C4—2982no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C4⋊C4—2981no—
132C4⋊C4—2981no—
133C4⋊C4—1492no—
134C4⋊C4—1491no—
135C4⋊C4D59611yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—2982no—
138C42—2981no—
139C42C22×D14911yescharacteristic
140C23—21no—
141Q8—2981no—
142Q8—5962no—
143Q8—5964no—
144Q8—5961no—
145Q8—5961no—
146Q8—1492no—
147D4—21no—
148D4Dic59612yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—2981no—
153C2×C4—2981no—
154C2×C4—2982no—
155C2×C4—5964no—
156C2×C4—5961no—
157C2×C4D4×D14911yescharacteristic
158C2×C4D4×D14911yescharacteristic
159C2×C4C2×D59611yescharacteristic
160C8—41no—
161C8—41no—
162C8—5961no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1801188111yescharacteristic
167C4—21no—
168C4—41no—
169C4—2982no—
170C4—5962no—
171C4—5961no—
172C4—11921no—
173C4SD16×D14911yescharacteristic
174C4C2×Dic59611yescharacteristic
175C4#1801193511yescharacteristic
176C4#1801194411yescharacteristic
177C2—42no—
178C2#2374977711yescharacteristic
179C2#2374978311yescharacteristic
180C2#2374979911yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
FittingD4⋊C8×C149C2
socleC22×C149#120
prime radicalC2×D4×C149D4
hypercenterD4⋊C8D149
hypocenterC149#1637
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #23749976C2semidirect
3. #23749921C2semidirect
5. #23749372C2semidirect
6. #23749357C2semidirect
90. C149#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2982
#237499762
#237499212
#237499152
#237493722
#237493572
D4⋊C8×C1492
#1637149