Finite Group Databasebeta

← #34043809

Subgroups — #34043809

Order 19072.

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

normal subgroups only

This group has 314 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×D596C211yesmaximal, characteristic
2#23749998C211yesmaximal, characteristic, complemented
3#23749916C211yesmaximal, characteristic, complemented
4#23749915C211yesmaximal, characteristic, complemented
5#23749368C211yesmaximal, characteristic, complemented
6#23749354C211yesmaximal, characteristic, complemented
7D4⋊C8×C149C211yesmaximal, characteristic, complemented
8C22×D596—21no—
9C2×D4×D149—21no—
10C2×#14558725—22no—
11#18011911C2211yescharacteristic, complemented
12#18011908C2211yescharacteristic
13#18011886—21no—
14#18011885—21no—
15#18011881—22no—
16C4×D596C2211yescharacteristic
17#18011843—21no—
18#18011842—21no—
19C4⋊#11924746C2211yescharacteristic, complemented
20#18011833—21no—
21#18011832—21no—
22C4×D4×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic, complemented
24C4×C8×C149C2211yescharacteristic, complemented
25C23×D149—22no—
26C2×Dic298—21no—
27C2×D596—22no—
28C2×D596—21no—
29C2×D596—21no—
30C2×D596—42no—
31C2×D596—42no—
32C2×D596D411yescharacteristic
33C2×D596D412yes—
34C2×C22⋊D149—22no—
35D4×D149—42no—
36D4×D149—42no—
37C2×C4×D149—21no—
38#14558725—44no—
39C2×#11924746—21no—
40C4⋊Dic149—21no—
41C4⋊Dic149—21no—
42C4⋊Dic149D411yescharacteristic
43#14558713—22no—
44#14558713—21no—
45C2×D4×C149D411yescharacteristic
46C22×C4×C149—21no—
47C2×C8×C149—21no—
48C2×C8×C149—21no—
49C4⋊C4×C149D411yescharacteristic
50C22⋊C4×C149—21no—
51C42×C149C2311yescharacteristic
52C22×D149—21no—
53C22×D149—22no—
54C22×D149—44no—
55C22×D149—44no—
56C22×D149—82no—
57Dic298—42no—
58D596—21no—
59D596—42no—
60D596—44no—
61D596—41no—
62D596—41no—
63D596—41no—
64D596—41no—
65D596SD1612yescomplemented
66C22⋊D149—44no—
67C2×Dic149—21no—
68C2×Dic149—41no—
69C4×D149—41no—
70C4×D149—41no—
71#11924746—41no—
72C23×C149—21no—
73D4×C149—21no—
74D4×C149SD1612yescomplemented
75C2×C4×C149—21no—
76C2×C4×C149—41no—
77C2×C4×C149—41no—
78C2×C4×C149C2×D411yescharacteristic
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D411yescharacteristic
81C8×C149—22no—
82C8×C149—41no—
83C22×C149—22no—
84C22×C149—41no—
85C22×C149—41no—
86C22×C149#12011yescharacteristic
87C2×D149—22no—
88C2×D149—41no—
89C2×D149—41no—
90C2×D149—42no—
91C2×D149—42no—
92C2×D149—42no—
93C2×D149—88no—
94C4×C149—21no—
95C4×C149—41no—
96C4×C149C2×SD1611yescharacteristic
97C4×C149C2×SD1611yescharacteristic
98C4×C149AGL(1,ℤ/8)11yescharacteristic
99C4×C149AGL(1,ℤ/8)11yescharacteristic
100Dic149—41no—
101Dic149—81no—
102C2×C149—42no—
103C2×C149#45011yescharacteristic
104C2×C149#45011yescharacteristic
105C2×C149#45311yescharacteristic
106D149—42no—
107D149—82no—
108C149#162911yescharacteristic, complemented, Sylow
109#1629—1491nomaximal, Sylow
110D42—1491no—
111#492—1491no—
112#476—1491no—
113#476—1491no—
114#331—1491no—
115D4⋊C8—1491no—
116D4⋊C8D14911yescharacteristic, complemented
117C22×D4—2981no—
118C22×D4—2981no—
119C2×SD16—2982no—
120C4⋊Q8—1491no—
121#127—1491no—
122#121—2981no—
123#121—2981no—
124#120—2982no—
125C4×D4—1491no—
126C4×D4C2×D14911yescharacteristic
127#106—2981no—
128#106—2981no—
129C4⋊C8—1491no—
130C4⋊C8C2×D14911yescharacteristic, complemented
131#102—2981no—
132#102—2981no—
133C4×C8C2×D14911yescharacteristic, complemented
134C24—2982no—
135C2×Q8—2981no—
136C2×D4—2982no—
137C2×D4—2982no—
138C2×D4—2981no—
139C2×D4—2981no—
140C2×D4—5962no—
141C2×D4—5962no—
142C2×D4—5962no—
143C2×D4—5962no—
144C2×D4—1491no—
145C2×D4—1492no—
146C2×D4D59611yescharacteristic
147C22×C4—21no—
148C22×C4—2981no—
149SD16—5964no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—2981no—
153C4⋊C4—2981no—
154C4⋊C4—2981no—
155C4⋊C4—1491no—
156C4⋊C4D59611yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—2982no—
159C22⋊C4—2981no—
160C42C22×D14911yescharacteristic
161C23—21no—
162C23—2981no—
163C23—2982no—
164C23—5964no—
165C23—5964no—
166C23—11922no—
167Q8—5962no—
168D4—21no—
169D4—2981no—
170D4—5962no—
171D4—5964no—
172D4—5964no—
173D4—5961no—
174D4—5961no—
175D4—5961no—
176D4—5961no—
177D4—1492no—
178D4#1455872512yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—2981no—
183C2×C4—5961no—
184C2×C4—5961no—
185C2×C4—5961no—
186C2×C4D4×D14911yescharacteristic
187C2×C4D4×D14911yescharacteristic
188C2×C4C2×D59611yescharacteristic
189C8—22no—
190C8—41no—
191C8—5961no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—2982no—
196C22—5961no—
197C22—5961no—
198C22—5962no—
199C22—5962no—
200C22—5962no—
201C22—11928no—
202C22#1801188111yescharacteristic
203C4—21no—
204C4—41no—
205C4—5961no—
206C4—11921no—
207C4SD16×D14911yescharacteristic
208C4C2×#1455872511yescharacteristic
209C4#1801193511yescharacteristic
210C4#1801193911yescharacteristic
211C2—42no—
212C2—5962no—
213C2—11922no—
214C2#2374977711yescharacteristic
215C2#2374977811yescharacteristic
216C2#2374979411yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
FittingD4⋊C8×C149C2
socleC22×C149#120
prime radicalD4×D596C2
hypercenterD4⋊C8D149
hypocenterC149#1629
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. #23749916C2semidirect
4. #23749915C2semidirect
5. #23749368C2semidirect
6. #23749354C2semidirect
7. D4⋊C8×C149C2semidirect
11. #18011911C22semidirect
19. C4⋊#11924746C22semidirect
23. C4⋊C8×C149C22semidirect
24. C4×C8×C149C22semidirect
65. D596SD16semidirect
74. D4×C149SD16semidirect
108. C149#1629semidirect
116. D4⋊C8D149semidirect
130. C4⋊C8C2×D149semidirect
133. C4×C8C2×D149semidirect
178. D4#14558725semidirect

Maximal subgroups

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

subgroupindex
D4×D5962
#237499982
#237499162
#237499152
#237493682
#237493542
D4⋊C8×C1492
#1629149