Finite Group Databasebeta

← #34060151

Subgroups — #34060151

Order 19072.

264 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750648C211yesmaximal, characteristic, complemented
2C4×#14558746C211yesmaximal, characteristic, complemented
3#23750481C212yesmaximal, complemented
4#23750480C212yesmaximal, complemented
5#124×D149C211yesmaximal, characteristic
6C2×#14558746—21no—
7#18011978—21no—
8#18011968—21no—
9#18011966C2212yescomplemented
10#18011966C2212yescomplemented
11C4×#11924753—21no—
12C2×Q8×D149C411yescharacteristic
13C2×D4×D149C411yescharacteristic
14#18011900C2211yescharacteristic
15#18011899C411yescharacteristic
16#18011898C2211yescharacteristic
17#18011897—21no—
18#18011897—21no—
19C22⋊C4×D149—21no—
20C22⋊C4×D149—21no—
21C42×D149C2211yescharacteristic
22#124×C149C411yescharacteristic
23#14558746—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C23×D149—21no—
27C2×Dic298—21no—
28C2×Dic298C2×C411yescharacteristic
29Q8×D149—42no—
30C2×D596C2×C411yescharacteristic
31C2×C22⋊D149—21no—
32D4×D149—42no—
33C2×C4×D149—21no—
34C2×C4×D149C2×C411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149D411yescharacteristic
37C22⋊Dic149—21no—
38C22⋊Dic149—21no—
39#14558713—21no—
40#14558713—21no—
41#14558713—21no—
42#14558713—21no—
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4×Dic149C2311yescharacteristic
46C2×Q8×C149C2×C411yescharacteristic
47C2×D4×C149C2×C411yescharacteristic
48C22⋊C4×C149—21no—
49C22⋊C4×C149—21no—
50C42×C149C2×C411yescharacteristic
51#11924753—24no—
52#11924753—42no—
53C22×D149—21no—
54C22×D149—42no—
55C22×D149—42no—
56C22×D149—42no—
57C22×D149C22⋊C411yescharacteristic
58Dic298—42no—
59Dic298—41no—
60D596—41no—
61C22⋊D149—42no—
62C2×Dic149—21no—
63C2×Dic149C22⋊C411yescharacteristic
64C2×Dic149C2×D411yescharacteristic
65C2×Dic149C2×D411yescharacteristic
66C4×D149—22no—
67C4×D149—22no—
68C4×D149—41no—
69C4×D149—42no—
70C23×C149—21no—
71Q8×C149—41no—
72D4×C149—41no—
73C2×C4×C149—21no—
74C2×C4×C149C22⋊C411yescharacteristic
75C2×C4×C149C22⋊C411yescharacteristic
76C2×C4×C149C22×C411yescharacteristic
77C22×C149—41no—
78C22×C149—41no—
79C22×C149—41no—
80C22×C149C2×C22⋊C411yescharacteristic
81C2×D149—21no—
82C2×D149—21no—
83C2×D149—41no—
84C2×D149—41no—
85C2×D149—41no—
86C2×D149—84no—
87C2×D149#10412yes—
88C4×C149—21no—
89C4×C149—21no—
90C4×C149—21no—
91C4×C149—41no—
92Dic149—21no—
93Dic149—21no—
94Dic149—41no—
95Dic149#10012yes—
96C2×C149—81no—
97C2×C149C2×#10011yescharacteristic
98C2×C149C2×#10411yescharacteristic
99C2×C149#42111yescharacteristic
100D149—22no—
101D149—81no—
102C149#152711yescharacteristic, complemented, Sylow
103#1527—1491nomaximal, Sylow
104C2×#124—1491no—
105#432—1491no—
106C4×M16—1491no—
107#329—1492no—
108#329—1492no—
109C22×Q8—1491no—
110C22×D4—1491no—
111C2×M16—2981no—
112#124—2981no—
113#124—2981no—
114#124—1491no—
115#124—1491no—
116#124—1491no—
117#124#1059701011yescharacteristic
118C2×C22⋊C4—2981no—
119C2×C22⋊C4—2981no—
120C2×C42—1491no—
121C4⋊C8—2981no—
122C22⋊C8—2981no—
123#97—1492no—
124#97—1492no—
125C4×C8—2981no—
126C24—2981no—
127C2×Q8—2981no—
128C2×Q8—5962no—
129C2×Q8—1491no—
130C2×Q8C2×#1059701011yescharacteristic
131C2×D4—2981no—
132C2×D4—5962no—
133C2×D4—1491no—
134C2×D4C2×#1059701011yescharacteristic
135C22×C4—2981no—
136C22×C4—1491no—
137C22×C4—1491no—
138C22×C4—1491no—
139M16—2984no—
140C2×C8—2982no—
141C2×C8—2982no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—2981no—
145C22⋊C4—2981no—
146C22⋊C4—2981no—
147C22⋊C4—2981no—
148C22⋊C4—2981no—
149C22⋊C4—2981no—
150C42—1491no—
151C42—1491no—
152C42—1491no—
153C42C2×#1059701011yescharacteristic
154C23—21no—
155C23—2981no—
156C23—5962no—
157C23—5962no—
158C23—5962no—
159C23—1491no—
160Q8—41no—
161Q8—5961no—
162Q8—5962no—
163D4—41no—
164D4—5961no—
165D4—5962no—
166C2×C4—21no—
167C2×C4—2982no—
168C2×C4—2982no—
169C2×C4—2981no—
170C2×C4—5961no—
171C2×C4—5962no—
172C2×C4—1491no—
173C2×C4—1491no—
174C2×C4—1491no—
175C2×C4C22⋊#1059701011yescharacteristic
176C2×C4C22⋊#1059701011yescharacteristic
177C2×C4C22×#1059701011yescharacteristic
178C8—2984no—
179C8—5962no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—2981no—
184C22—2981no—
185C22—5961no—
186C22—5961no—
187C22—5961no—
188C22—1492no—
189C22—11924no—
190C22C2×C22⋊#1059701011yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—41no—
195C4—2981no—
196C4—2981no—
197C4—5961no—
198C4—1492no—
199C2—81no—
200C2—2982no—
201C2—11921no—
202C2D149⋊#10011yescharacteristic
203C2D149⋊#10411yescharacteristic
204C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×D4×D149C4
cosocleC4×Dic149C23
hypercenter#124#10597010
hypocenterC149#1527
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #23750648C2semidirect
2. C4×#14558746C2semidirect
3. #23750481C2semidirect
4. #23750480C2semidirect
9. #18011966C22semidirect
10. #18011966C22semidirect
102. C149#1527semidirect

Maximal subgroups

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

subgroupindex
#237506482
C4×#145587462
#237504812
#237504802
#124×D1492
#1527149