Finite Group Databasebeta

← #34043313

Subgroups — #34043313

Order 19072.

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

normal subgroups only

This group has 248 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
1#124×D149C211yesmaximal, characteristic
2#23749680C212yesmaximal, complemented
3#23749365C211yesmaximal, characteristic, complemented
4#23749364C212yesmaximal, complemented
5#329×C149C211yesmaximal, characteristic, complemented
6C2×Q8×D149C411yescharacteristic
7C2×D4×D149C411yescharacteristic
8#18011900C411yescharacteristic
9#18011899C2211yescharacteristic
10#18011898C411yescharacteristic
11#18011897—22no—
12C22⋊C4×D149—22no—
13C42×D149C2211yescharacteristic
14#18011840—22no—
15#18011823—22no—
16#18011822C2212yescomplemented
17#124×C149C2211yescharacteristic
18#97×C149C2212yescomplemented
19C23×D149—21no—
20C2×Dic298—21no—
21C2×Dic298C2×C411yescharacteristic
22Q8×D149—42no—
23C2×D596C2×C411yescharacteristic
24C2×C22⋊D149—21no—
25D4×D149—42no—
26C2×C4×D149—21no—
27C2×C4×D149C2×C411yescharacteristic
28C2×C4×D149D412yes—
29C2×#11924746—22no—
30C22⋊Dic149—22no—
31#14558713—22no—
32#14558713—22no—
33C4×Dic149C2×C411yescharacteristic
34C4×Dic149D412yes—
35C2×Q8×C149C2×C411yescharacteristic
36C2×D4×C149C2×C411yescharacteristic
37C2×C8×C149—22no—
38C22⋊C4×C149—22no—
39C42×C149C2311yescharacteristic
40C22×D149—21no—
41C22×D149—44no—
42C22×D149—42no—
43C22×D149C22⋊C411yescharacteristic
44Dic298—42no—
45Dic298—41no—
46D596—41no—
47C22⋊D149—42no—
48C2×Dic149—21no—
49C2×Dic149C22⋊C411yescharacteristic
50C2×Dic149C22⋊C412yes—
51C4×D149—22no—
52C4×D149—42no—
53C4×D149—42no—
54#11924746—42no—
55C23×C149—21no—
56Q8×C149—41no—
57D4×C149—41no—
58C2×C4×C149—21no—
59C2×C4×C149C22×C411yescharacteristic
60C2×C4×C149C2×D412yes—
61C8×C149—42no—
62C22×C149—41no—
63C22×C149—42no—
64C22×C149C2×C22⋊C411yescharacteristic
65C2×D149—22no—
66C2×D149—41no—
67C2×D149—42no—
68C2×D149—84no—
69C2×D149#10012yes—
70C4×C149—21no—
71C4×C149—22no—
72C4×C149—41no—
73Dic149—21no—
74Dic149—22no—
75Dic149—41no—
76C2×C149—81no—
77C2×C149C2×#10011yescharacteristic
78C2×C149#42112yes—
79D149—22no—
80D149—81no—
81C149#153311yescharacteristic, complemented, Sylow
82#1533—1491nomaximal, Sylow
83C2×#124—1491no—
84#432—1492no—
85#329—1491no—
86#329—1492no—
87#329D14911yescharacteristic, complemented
88C22×Q8—1491no—
89C22×D4—1491no—
90#124—2982no—
91#124—1491no—
92#124—1491no—
93#124—1491no—
94#124C2×D14911yescharacteristic
95C2×C22⋊C4—2982no—
96C2×C42—1491no—
97C4⋊C8—2982no—
98C22⋊C8—2982no—
99#97—1492no—
100#97C2×D14912yescomplemented
101C24—2981no—
102C2×Q8—2981no—
103C2×Q8—5962no—
104C2×Q8—1491no—
105C2×Q8C4×D14911yescharacteristic
106C2×D4—2981no—
107C2×D4—5962no—
108C2×D4—1491no—
109C2×D4C4×D14911yescharacteristic
110C22×C4—2981no—
111C22×C4—1491no—
112C22×C4—1492no—
113C2×C8—22no—
114C2×C8—2982no—
115C22⋊C4—22no—
116C22⋊C4—2982no—
117C22⋊C4—2982no—
118C22⋊C4—2982no—
119C42—1491no—
120C42—1492no—
121C42C22×D14911yescharacteristic
122C23—21no—
123C23—2981no—
124C23—5964no—
125C23—5962no—
126C23—1491no—
127Q8—41no—
128Q8—5961no—
129Q8—5962no—
130D4—41no—
131D4—5961no—
132D4—5962no—
133C2×C4—21no—
134C2×C4—2982no—
135C2×C4—2981no—
136C2×C4—5962no—
137C2×C4—5962no—
138C2×C4—1492no—
139C2×C4—1491no—
140C2×C4C2×C4×D14911yescharacteristic
141C2×C4D4×D14912yes—
142C8—42no—
143C8—5962no—
144C22—42no—
145C22—41no—
146C22—2982no—
147C22—5962no—
148C22—5961no—
149C22—1492no—
150C22—11924no—
151C22C22⋊C4×D14911yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—2982no—
156C4—2981no—
157C4—5961no—
158C2—81no—
159C2—2982no—
160C2—11921no—
161C2#100×D14911yescharacteristic
162C2#2374964012yes—
subgroupG/H
centerC22C22⋊C4×D149
commutatorC2×C4×C149C22×C4
FrattiniC42C22×D149
Fitting#329×C149C2
socleC22×C149C2×C22⋊C4
prime radicalC2×D4×D149C4
cosocleC42×C149C23
hypercenter#329D149
hypocenterC149#1533
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23749680C2semidirect
3. #23749365C2semidirect
4. #23749364C2semidirect
5. #329×C149C2semidirect
16. #18011822C22semidirect
18. #97×C149C22semidirect
81. C149#1533semidirect
87. #329D149semidirect
100. #97C2×D149semidirect

Maximal subgroups

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

subgroupindex
#124×D1492
#237496802
#237493652
#237493642
#329×C1492
#1533149