Finite Group Databasebeta

← D149⋊#353 #34060957

Subgroups — D149⋊#353 #34060957

Order 19072.

368 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D149⋊#99C212yesmaximal, complemented
2#23750530C212yesmaximal, complemented
3#23750529C212yesmaximal, complemented
4#127×D149C211yesmaximal, characteristic
5C2×C22⋊#10597010—22no—
6#18011970C2214yescomplemented
7#18011969—22no—
8C2×D4×D149—22no—
9C2×D4×D149C411yescharacteristic, complemented
10C2×D4×D149C2211yescharacteristic
11#18011908C2211yescharacteristic
12#18011907—22no—
13#18011907C411yescharacteristic, complemented
14#18011907C2211yescharacteristic
15C42×D149C411yescharacteristic, complemented
16#127×C149C411yescharacteristic, complemented
17C22×#10597010—42no—
18C22⋊#10597010—24no—
19C22⋊#10597010—42no—
20C23×D149—21no—
21C23×D149D412yes—
22C2×D596—22no—
23C2×D596C2×C411yescharacteristic, complemented
24C2×D596C2311yescharacteristic
25C2×C22⋊D149—22no—
26C2×C22⋊D149—21no—
27C2×C22⋊D149—22no—
28C2×C22⋊D149D412yes—
29D4×D149—41no—
30D4×D149—41no—
31D4×D149—48no—
32D4×D149—41no—
33D4×D149—41no—
34C2×C4×D149—21no—
35C2×C4×D149C2×C411yescharacteristic
36C4×Dic149—21no—
37C4×Dic149C2×C411yescharacteristic, complemented
38C2×D4×C149—22no—
39C2×D4×C149C2×C411yescharacteristic
40C2×D4×C149C2×C411yescharacteristic, complemented
41C42×C149C2×C411yescharacteristic, complemented
42C2×#10597010—44no—
43C2×#10597010—84no—
44C22×D149—22no—
45C22×D149—22no—
46C22×D149—21no—
47C22×D149—44no—
48C22×D149—44no—
49C22×D149—41no—
50C22×D149—41no—
51C22×D149C22⋊C411yescharacteristic
52C22×D149C2×D412yes—
53D596—41no—
54D596—41no—
55D596—44no—
56C22⋊D149—42no—
57C22⋊D149—44no—
58C22⋊D149—44no—
59C22⋊D149—42no—
60C2×Dic149—21no—
61C2×Dic149C22⋊C411yescharacteristic
62C4×D149—24no—
63C4×D149—21no—
64C4×D149—21no—
65C23×C149—21no—
66C23×C149C22⋊C412yes—
67D4×C149—41no—
68D4×C149—41no—
69D4×C149—44no—
70C2×C4×C149—21no—
71C2×C4×C149C22×C411yescharacteristic
72C22×C149—22no—
73C22×C149—42no—
74C22×C149—42no—
75C22×C149—41no—
76C22×C149C2×C22⋊C411yescharacteristic
77C2×D149—22no—
78C2×D149—22no—
79C2×D149—44no—
80C2×D149—42no—
81C2×D149—42no—
82C2×D149—41no—
83C2×D149—82no—
84C2×D149—82no—
85C2×D149—82no—
86C2×D149#9911yescharacteristic
87C2×D149#9911yescharacteristic
88#10597010—84no—
89C4×C149—22no—
90C4×C149—21no—
91Dic149—22no—
92Dic149—21no—
93C2×C149—21no—
94C2×C149—42no—
95C2×C149—81no—
96C2×C149C2×#9911yescharacteristic
97D149—21no—
98D149—42no—
99D149—81no—
100D149#35312yescomplemented
101C149C2×#35311yescharacteristic, complemented, Sylow
102C2×#353—1491nomaximal, Sylow
103C2×#127—1491no—
104C2×#99—1492no—
105#353—1492no—
106#353—1492no—
107C22×D4—2982no—
108C22×D4—1491no—
109C22×D4—1491no—
110#127—2982no—
111#127—1491no—
112#127—1491no—
113#127—1491no—
114#127#1059701011yescharacteristic, complemented
115C2×C22⋊C4—2982no—
116C2×C42—1491no—
117#99—2982no—
118#99—1494no—
119C24—2981no—
120C24—1492no—
121C2×D4—22no—
122C2×D4—2982no—
123C2×D4—2982no—
124C2×D4—2982no—
125C2×D4—2981no—
126C2×D4—5961no—
127C2×D4—5961no—
128C2×D4—5961no—
129C2×D4—5961no—
130C2×D4—5968no—
131C2×D4—1492no—
132C2×D4—1491no—
133C2×D4—1491no—
134C2×D4C2×#1059701011yescharacteristic
135C2×D4C2×#1059701011yescharacteristic, complemented
136C22×C4—2981no—
137C22×C4—5962no—
138C22×C4—1491no—
139C22⋊C4—2984no—
140C22⋊C4—5962no—
141C42—2981no—
142C42—1491no—
143C42C2×#1059701011yescharacteristic, complemented
144C23—21no—
145C23—2982no—
146C23—2982no—
147C23—2981no—
148C23—5964no—
149C23—5964no—
150C23—5961no—
151C23—5961no—
152C23—1491no—
153C23—1492no—
154C23C22⋊#1059701012yes—
155D4—41no—
156D4—41no—
157D4—44no—
158D4—5961no—
159D4—5961no—
160D4—5964no—
161D4—5962no—
162D4—5964no—
163D4—5964no—
164D4—5962no—
165C2×C4—21no—
166C2×C4—2984no—
167C2×C4—2981no—
168C2×C4—2981no—
169C2×C4—2981no—
170C2×C4—5964no—
171C2×C4—1491no—
172C2×C4—11924no—
173C2×C4C22×#1059701011yescharacteristic
174C22—22no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—2982no—
179C22—2982no—
180C22—5962no—
181C22—5962no—
182C22—5964no—
183C22—5961no—
184C22—1491no—
185C22—1491no—
186C22—11922no—
187C22—11922no—
188C22—11922no—
189C22C2×C22⋊#1059701011yescharacteristic
190C4—22no—
191C4—21no—
192C4—2982no—
193C4—2981no—
194C4—11924no—
195C2—21no—
196C2—42no—
197C2—81no—
198C2—2981no—
199C2—5962no—
200C2—1492no—
201C2—11921no—
202C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC2×C149C2×#99
prime radical#127×D149C2
cosocleC2×D596C23
hypercenter#127#10597010
hypocenterC149C2×#353
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. D149⋊#99C2semidirect
2. #23750530C2semidirect
3. #23750529C2semidirect
6. #18011970C22semidirect
9. C2×D4×D149C4semidirect
13. #18011907C4semidirect
15. C42×D149C4semidirect
16. #127×C149C4semidirect
23. C2×D596C2×C4semidirect
37. C4×Dic149C2×C4semidirect
40. C2×D4×C149C2×C4semidirect
41. C42×C149C2×C4semidirect
100. D149#353semidirect
101. C149C2×#353semidirect
114. #127#10597010semidirect
135. C2×D4C2×#10597010semidirect
143. C42C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊#992
#237505302
#237505292
#127×D1492
C2×#353149