Finite Group Databasebeta

← #34043821

Subgroups — #34043821

Order 19072.

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

normal subgroups only

This group has 256 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#23750296C211yesmaximal, characteristic
2#23749998C211yesmaximal, characteristic, complemented
3#23749921C211yesmaximal, characteristic, complemented
4#23749915C211yesmaximal, characteristic, complemented
5#23749368C211yesmaximal, characteristic, complemented
6#23749357C211yesmaximal, characteristic, complemented
7D4⋊C8×C149C211yesmaximal, characteristic, complemented
8C2×#14558736—21no—
9C2×#14558725—22no—
10#18011911C2211yescharacteristic
11#18011908C2211yescharacteristic
12#18011907—21no—
13#18011885—21no—
14#18011884—22no—
15C4×Dic298C2211yescharacteristic
16#18011873—21no—
17#18011845—21no—
18#18011842—21no—
19C4⋊#11924746C2211yescharacteristic
20#18011836—21no—
21#18011832—21no—
22C4×D4×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4×C8×C149C2211yescharacteristic
25#14558736—42no—
26#14558736—42no—
27C2×Dic298—21no—
28C2×Dic298D411yescharacteristic
29C2×D596—21no—
30C2×D596—21no—
31C2×D596D412yes—
32C2×C22⋊D149—22no—
33C2×C22⋊D149—22no—
34C2×C4×D149—22no—
35#14558725—44no—
36C2×#11924746—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149—21no—
39C4⋊Dic149D411yescharacteristic
40#14558715—21no—
41#14558713—22no—
42C4×Dic149—21no—
43C2×D4×C149D411yescharacteristic
44C22×C4×C149—21no—
45C2×C8×C149—21no—
46C2×C8×C149—21no—
47C4⋊C4×C149D411yescharacteristic
48C22⋊C4×C149—21no—
49C42×C149C2311yescharacteristic
50C22×D149—22no—
51Dic298—21no—
52Dic298—42no—
53Dic298SD1612yescomplemented
54D596—42no—
55D596—41no—
56D596—41no—
57D596—41no—
58D596—41no—
59C22⋊D149—44no—
60C22⋊D149—82no—
61C2×Dic149—21no—
62C2×Dic149—21no—
63C2×Dic149—41no—
64C4×D149—44no—
65#11924746—41no—
66C23×C149—21no—
67D4×C149—21no—
68D4×C149—21no—
69C2×C4×C149—21no—
70C2×C4×C149—41no—
71C2×C4×C149—41no—
72C2×C4×C149C2×D411yescharacteristic
73C2×C4×C149C2×D411yescharacteristic
74C2×C4×C149C2×D411yescharacteristic
75C8×C149—22no—
76C8×C149—41no—
77C22×C149—41no—
78C22×C149—41no—
79C22×C149—41no—
80C22×C149#12011yescharacteristic
81C2×D149—42no—
82C2×D149—42no—
83C2×D149—42no—
84C4×C149—21no—
85C4×C149—41no—
86C4×C149C2×SD1611yescharacteristic
87C4×C149#13511yescharacteristic
88C4×C149AGL(1,ℤ/8)11yescharacteristic
89C4×C149#13711yescharacteristic
90Dic149—22no—
91Dic149—41no—
92Dic149—81no—
93C2×C149—81no—
94C2×C149#45011yescharacteristic
95C2×C149#45211yescharacteristic
96C2×C149#45311yescharacteristic
97D149—82no—
98C149#163111yescharacteristic, complemented, Sylow
99#1631—1491nomaximal, Sylow
100#550—1491no—
101#492—1491no—
102#477—1491no—
103#476—1491no—
104#331—1491no—
105Q8⋊C8—1491no—
106D4⋊C8D14911yescharacteristic, complemented
107C2×#41—2981no—
108C2×SD16—2982no—
109C4⋊Q8—1491no—
110#127—2981no—
111#127—1491no—
112#121—2982no—
113#121—2981no—
114C4×Q8—1491no—
115C4×D4—2981no—
116C4×D4C2×D14911yescharacteristic
117#107—2981no—
118#106—2981no—
119C4⋊C8—1491no—
120C4⋊C8C2×D14911yescharacteristic
121#103—2981no—
122#102—2981no—
123C4×C8C2×D14911yescharacteristic
124#41—5962no—
125#41—5962no—
126C2×Q8—2981no—
127C2×Q8—1491no—
128C2×D4—2982no—
129C2×D4—2982no—
130C2×D4—2981no—
131C2×D4—2981no—
132C2×D4—1492no—
133C2×D4D59611yescharacteristic
134C22×C4—21no—
135C22×C4—2982no—
136SD16—5964no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—2981no—
140C4⋊C4—2981no—
141C4⋊C4—2981no—
142C4⋊C4—2981no—
143C4⋊C4—1491no—
144C4⋊C4D59611yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—2982no—
147C42—2981no—
148C42C22×D14911yescharacteristic
149C23—21no—
150C23—2982no—
151Q8—2981no—
152Q8—5962no—
153Q8—1492no—
154D4—21no—
155D4—21no—
156D4—5962no—
157D4—5964no—
158D4—5961no—
159D4—5961no—
160D4—5961no—
161D4—5961no—
162D4—11922no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—2981no—
167C2×C4—2981no—
168C2×C4—5964no—
169C2×C4—5961no—
170C2×C4D4×D14911yescharacteristic
171C2×C4D4×D14911yescharacteristic
172C2×C4C2×D59611yescharacteristic
173C8—22no—
174C8—41no—
175C8—5961no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—5962no—
180C22—5962no—
181C22—5962no—
182C22#1801188111yescharacteristic
183C4—21no—
184C4—41no—
185C4—2982no—
186C4—5961no—
187C4—11921no—
188C4SD16×D14911yescharacteristic
189C4#1801193311yescharacteristic
190C4#1801193511yescharacteristic
191C4#1801194411yescharacteristic
192C2—81no—
193C2—11922no—
194C2#2374977711yescharacteristic
195C2#2374978911yescharacteristic
196C2#2374979411yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
FittingD4⋊C8×C149C2
socleC22×C149#120
prime radical#23750296C2
hypercenterD4⋊C8D149
hypocenterC149#1631
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. #23749998C2semidirect
3. #23749921C2semidirect
4. #23749915C2semidirect
5. #23749368C2semidirect
6. #23749357C2semidirect
7. D4⋊C8×C149C2semidirect
53. Dic298SD16semidirect
98. C149#1631semidirect
106. D4⋊C8D149semidirect

Maximal subgroups

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

subgroupindex
#237502962
#237499982
#237499212
#237499152
#237493682
#237493572
D4⋊C8×C1492
#1631149