Finite Group Databasebeta

← #34043845

Subgroups — #34043845

Order 19072.

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

normal subgroups only

This group has 234 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#23750280C211yesmaximal, characteristic
2#23749976C211yesmaximal, characteristic, complemented
3#23749916C211yesmaximal, characteristic, complemented
4#23749915C211yesmaximal, characteristic, complemented
5#23749372C211yesmaximal, characteristic, complemented
6#23749354C211yesmaximal, characteristic, complemented
7D4⋊C8×C149C211yesmaximal, characteristic, complemented
8C2×#14558736—21no—
9#18011911C2211yescharacteristic
10#18011911C2211yescharacteristic
11#18011893—22no—
12#18011890—21no—
13#18011882—21no—
14C4×D596C2211yescharacteristic
15C4⋊C4×D149—21no—
16#18011843—21no—
17#18011842—21no—
18C4⋊#11924746C2211yescharacteristic
19#18011836—22no—
20#18011833—21no—
21#18011832—21no—
22C4×D4×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4×C8×C149C2211yescharacteristic
25#14558736—42no—
26#14558736—42no—
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×D596D411yescharacteristic
30C2×C22⋊D149—22no—
31C2×C4×D149—22no—
32C2×C4×D149—21no—
33C2×#11924746—21no—
34C4⋊Dic149—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149—21no—
37C4⋊Dic149D412yes—
38C4⋊Dic149D411yescharacteristic
39#14558715—22no—
40C22⋊Dic149—22no—
41#14558713—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
49C22×D149—21no—
50Dic298—41no—
51Dic298—41no—
52Dic298—42no—
53D596—21no—
54D596SD1612yes—
55C22⋊D149—44no—
56C2×Dic149—22no—
57C2×Dic149—21no—
58C2×Dic149—41no—
59C4×D149—44no—
60C4×D149—41no—
61C4×D149—41no—
62#11924746—41no—
63C23×C149—21no—
64D4×C149—21no—
65D4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149—41no—
68C2×C4×C149—41no—
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149C2×D411yescharacteristic
71C2×C4×C149C2×D411yescharacteristic
72C8×C149—41no—
73C8×C149—41no—
74C22×C149—41no—
75C22×C149—41no—
76C22×C149—41no—
77C22×C149#12011yescharacteristic
78C2×D149—22no—
79C2×D149—41no—
80C2×D149—41no—
81C4×C149—21no—
82C4×C149—41no—
83C4×C149C2×SD1611yescharacteristic
84C4×C149#13511yescharacteristic
85C4×C149AGL(1,ℤ/8)11yescharacteristic
86C4×C149#13711yescharacteristic
87Dic149—42no—
88Dic149—41no—
89Dic149—81no—
90C2×C149—81no—
91C2×C149#45011yescharacteristic
92C2×C149#45211yescharacteristic
93C2×C149#45411yescharacteristic
94D149—42no—
95C149#163511yescharacteristic, complemented, Sylow
96#1635—1491nomaximal, Sylow
97#547—1491no—
98#487—1491no—
99#476—1491no—
100#476—1491no—
101#332—1491no—
102D4⋊C8—1491no—
103D4⋊C8D14911yescharacteristic, complemented
104C2×#41—2981no—
105C4⋊Q8—1491no—
106C4⋊Q8—1491no—
107#123—2982no—
108C22⋊Q8—2981no—
109#121—2981no—
110C4×D4—1491no—
111C4×D4C2×D14911yescharacteristic
112C2×C4⋊C4—2981no—
113#106—2981no—
114#106—2981no—
115C4⋊C8—1491no—
116C4⋊C8C2×D14911yescharacteristic
117#103—2982no—
118#102—2981no—
119#102—2981no—
120C4×C8C2×D14911yescharacteristic
121#41—5962no—
122#41—5962no—
123C2×Q8—2981no—
124C2×Q8—2981no—
125C2×D4—2982no—
126C2×D4—1491no—
127C2×D4D59611yescharacteristic
128C22×C4—21no—
129C22×C4—2982no—
130C22×C4—2981no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—2981no—
134C4⋊C4—2982no—
135C4⋊C4—2981no—
136C4⋊C4—2981no—
137C4⋊C4—2981no—
138C4⋊C4—1492no—
139C4⋊C4—1491no—
140C4⋊C4D59611yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—2982no—
143C22⋊C4—2981no—
144C42C22×D14911yescharacteristic
145C23—21no—
146C23—2981no—
147Q8—5962no—
148Q8—5961no—
149Q8—5961no—
150D4—21no—
151D4—21no—
152D4—2981no—
153D4—5964no—
154D4—1492no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—2981no—
159C2×C4—2982no—
160C2×C4—5964no—
161C2×C4—5961no—
162C2×C4—5961no—
163C2×C4—5961no—
164C2×C4D4×D14911yescharacteristic
165C2×C4D4×D14911yescharacteristic
166C2×C4C2×D59611yescharacteristic
167C8—41no—
168C8—41no—
169C8—5961no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—2982no—
174C22—5961no—
175C22—5961no—
176C22#1801188111yescharacteristic
177C4—21no—
178C4—41no—
179C4—5962no—
180C4—5961no—
181C4—11921no—
182C4SD16×D14911yescharacteristic
183C4#1801193311yescharacteristic
184C4#1801193511yescharacteristic
185C4#1801194411yescharacteristic
186C2—81no—
187C2—5962no—
188C2#2374977711yescharacteristic
189C2#2374978911yescharacteristic
190C2#2374979911yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
FittingD4⋊C8×C149C2
socleC22×C149#120
prime radical#23750280C2
hypercenterD4⋊C8D149
hypocenterC149#1635
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. #23749916C2semidirect
4. #23749915C2semidirect
5. #23749372C2semidirect
6. #23749354C2semidirect
7. D4⋊C8×C149C2semidirect
95. C149#1635semidirect
103. D4⋊C8D149semidirect

Maximal subgroups

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

subgroupindex
#237502802
#237499762
#237499162
#237499152
#237493722
#237493542
D4⋊C8×C1492
#1635149