Finite Group Databasebeta

← #34060826

Subgroups — #34060826

Order 19072.

360 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 74 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#23750630C211yesmaximal, characteristic, complemented
2C2×#18011976C212yesmaximal, complemented
3C2×#18011975C212yesmaximal, complemented
4C42×#10597010C211yesmaximal, characteristic, complemented
5#23750174C211yesmaximal, characteristic
6C2×#14558746C2212yes—
7C2×C4×#10597010—22no—
8C2×C4×#10597010C2212yes—
9#18011978—22no—
10#18011976—24no—
11#18011975—24no—
12C2×#14558737C2211yescharacteristic
13C2×#14558735C2211yescharacteristic
14#18011909C411yescharacteristic, complemented
15#18011907C411yescharacteristic, complemented
16#18011899C411yescharacteristic, complemented
17#18011884—22no—
18#18011871—22no—
19C42×D149C2211yescharacteristic
20#124×C149C411yescharacteristic, complemented
21C22×#10597010—22no—
22#14558746—22no—
23#14558746—22no—
24C2×#11924753—22no—
25C4×#10597010—28no—
26C4×#10597010—22no—
27C4×#10597010D414yescomplemented
28#14558737—22no—
29#14558737—22no—
30#14558735—22no—
31#14558735—22no—
32C2×Dic298C2×C411yescharacteristic
33C2×D596—21no—
34C2×D596C2×C411yescharacteristic
35C2×C22⋊D149—21no—
36C2×C22⋊D149—22no—
37C22×Dic149—21no—
38C2×C4×D149—21no—
39C2×C4×D149D412yes—
40C2×C4×D149C2311yescharacteristic
41#14558715—22no—
42#14558713—22no—
43C4×Dic149C2×C411yescharacteristic
44C4×Dic149D412yes—
45C2×Q8×C149C2×C411yescharacteristic
46C2×D4×C149C2×C411yescharacteristic
47C22⋊C4×C149—22no—
48C42×C149C2×C411yescharacteristic
49C2×#10597010—28no—
50C2×#10597010—24no—
51#11924753—42no—
52C22×D149—21no—
53C22×D149C2×D411yescharacteristic
54Dic298—22no—
55D596—22no—
56D596—42no—
57C22⋊D149—42no—
58C22⋊D149—44no—
59C2×Dic149—21no—
60C2×Dic149—41no—
61C2×Dic149—41no—
62C2×Dic149C22⋊C412yes—
63C2×Dic149C2×D411yescharacteristic
64C4×D149—24no—
65C4×D149—41no—
66C4×D149—41no—
67C4×D149C2×D412yes—
68C4×D149#4112yes—
69C23×C149—21no—
70Q8×C149—22no—
71D4×C149—22no—
72C2×C4×C149—21no—
73C2×C4×C149C22⋊C412yes—
74C2×C4×C149C22×C411yescharacteristic
75C22×C149—41no—
76C22×C149—42no—
77C22×C149C2×C22⋊C411yescharacteristic
78C2×D149—22no—
79C2×D149—41no—
80C2×D149—42no—
81C2×D149#12112yes—
82#10597010—28no—
83C4×C149—22no—
84C4×C149—41no—
85C4×C149C4×D412yes—
86Dic149—41no—
87Dic149#10414yescomplemented
88Dic149#12411yescharacteristic
89Dic149#12711yescharacteristic
90C2×C149—81no—
91C2×C149#39011yescharacteristic
92C2×C149C2×#10412yes—
93D149—22no—
94D149—81no—
95C149#196211yescharacteristic, complemented, Sylow
96#1962—1491nomaximal, Sylow
97#532—1491no—
98#423—1491no—
99C2×#104—1492no—
100C2×#104—1492no—
101C43—1491no—
102C2×#41—1491no—
103C2×#41—1491no—
104C2×M16—1492no—
105C4⋊Q8—1491no—
106#127—1491no—
107#124—1491no—
108#124#1059701011yescharacteristic, complemented
109#121—2982no—
110C4×D4—2982no—
111C2×C42—2982no—
112C2×C42—1492no—
113C2×C42—1491no—
114C4⋊C8—2982no—
115#104—2984no—
116#104—2984no—
117#41—2982no—
118#41—2982no—
119#41—2982no—
120#41—2982no—
121C2×Q8—1491no—
122C2×Q8C2×#1059701011yescharacteristic
123C2×D4—2981no—
124C2×D4—2981no—
125C2×D4—2982no—
126C2×D4—1491no—
127C2×D4C2×#1059701011yescharacteristic
128C22×C4—2981no—
129C22×C4—2982no—
130C22×C4—2981no—
131C22×C4—1492no—
132C22×C4—1491no—
133M16—2982no—
134M16—2982no—
135C2×C8—2982no—
136C4⋊C4—2982no—
137C22⋊C4—22no—
138C22⋊C4—2982no—
139C42—2988no—
140C42—2982no—
141C42—1494no—
142C42—1492no—
143C42—1491no—
144C42C2×#1059701011yescharacteristic
145C23—21no—
146C23—2981no—
147C23—1491no—
148Q8—22no—
149Q8—2982no—
150D4—22no—
151D4—2982no—
152D4—5962no—
153D4—5962no—
154D4—5964no—
155C2×C4—21no—
156C2×C4—2984no—
157C2×C4—2988no—
158C2×C4—2984no—
159C2×C4—2981no—
160C2×C4—5961no—
161C2×C4—5961no—
162C2×C4—5961no—
163C2×C4—5961no—
164C2×C4—1492no—
165C2×C4—1491no—
166C2×C4—1492no—
167C2×C4—1492no—
168C2×C4C22⋊#1059701012yes—
169C2×C4C22×#1059701011yescharacteristic
170C8—5962no—
171C22—41no—
172C22—42no—
173C22—2982no—
174C22—5961no—
175C22—5962no—
176C22—1492no—
177C22C2×C22⋊#1059701011yescharacteristic
178C4—22no—
179C4—41no—
180C4—2988no—
181C4—5961no—
182C4—1491no—
183C4—1491no—
184C4—1494no—
185C4D4×#1059701012yes—
186C2—81no—
187C2—2982no—
188C2—11921no—
189C2#2375057711yescharacteristic
190C2D149⋊#10412yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750174C2
cosocleC2×C4×D149C23
hypercenter#124#10597010
hypocenterC149#1962
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #23750630C2semidirect
2. C2×#18011976C2semidirect
3. C2×#18011975C2semidirect
4. C42×#10597010C2semidirect
14. #18011909C4semidirect
15. #18011907C4semidirect
16. #18011899C4semidirect
20. #124×C149C4semidirect
27. C4×#10597010D4semidirect
87. Dic149#104semidirect
95. C149#1962semidirect
108. #124#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506302
C2×#180119762
C2×#180119752
C42×#105970102
#237501742
#1962149