Finite Group Databasebeta

← #34060968

Subgroups — #34060968

Order 19072.

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

normal subgroups only

This group has 286 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
1C2×#18011970C212yesmaximal, complemented
2#23750532C212yesmaximal, complemented
3#23750530C212yesmaximal, complemented
4#23750194C211yesmaximal, characteristic
5C2×C22⋊#10597010—22no—
6#18011970—22no—
7#18011970C2214yes—
8C2×#14558736C411yescharacteristic, complemented
9C22×D596C2211yescharacteristic
10#18011908C411yescharacteristic, complemented
11#18011908C2211yescharacteristic
12#18011899C411yescharacteristic, complemented
13#18011899C2211yescharacteristic
14#18011886—22no—
15#18011881—22no—
16#117×C149C411yescharacteristic, complemented
17C22×#10597010—42no—
18C22⋊#10597010—24no—
19C22⋊#10597010—42no—
20C23×D149D412yes—
21#14558736—42no—
22C2×Dic298C2×C411yescharacteristic, complemented
23C2×D596—22no—
24C2×D596—22no—
25C2×D596—42no—
26C2×D596C2×C411yescharacteristic
27C2×D596C2×C411yescharacteristic, complemented
28C2×D596D412yes—
29C2×D596C2311yescharacteristic
30C2×C22⋊D149—21no—
31C2×C4×D149—21no—
32#14558713—22no—
33#14558713—22no—
34C22×C4×C149C2×C411yescharacteristic
35C4⋊C4×C149—21no—
36C22⋊C4×C149—21no—
37C42×C149C2×C411yescharacteristic, complemented
38C42×C149C2×C411yescharacteristic, complemented
39C2×#10597010—44no—
40C2×#10597010—84no—
41C22×D149—22no—
42C22×D149—22no—
43C22×D149—21no—
44C22×D149—82no—
45C22×D149C22⋊C412yes—
46C22×D149C2×D412yes—
47Dic298—41no—
48D596—41no—
49D596—42no—
50D596—41no—
51D596—41no—
52D596—82no—
53D596—82no—
54C22⋊D149—42no—
55C2×Dic149—21no—
56C4×D149—42no—
57C23×C149C22⋊C411yescharacteristic
58C2×C4×C149—22no—
59C2×C4×C149—21no—
60C2×C4×C149—21no—
61C2×C4×C149C22⋊C411yescharacteristic
62C2×C4×C149C22×C411yescharacteristic
63C22×C149—41no—
64C22×C149#9912yes—
65C22×C149C2×C22⋊C411yescharacteristic
66C2×D149—22no—
67C2×D149—22no—
68C2×D149—44no—
69C2×D149—42no—
70C2×D149—42no—
71C2×D149—42no—
72C2×D149—41no—
73C2×D149—82no—
74#10597010—84no—
75C4×C149—21no—
76C4×C149—21no—
77C4×C149—41no—
78C4×C149—41no—
79Dic149—41no—
80C2×C149—21no—
81C2×C149—22no—
82C2×C149C2×#9911yescharacteristic
83D149—42no—
84D149—42no—
85D149—81no—
86C149#212711yescharacteristic, complemented, Sylow
87#2127—1491nomaximal, Sylow
88#535—1491no—
89C2×#99—1492no—
90#354—1492no—
91#353—1492no—
92C2×#41—1491no—
93C22×D4—1491no—
94#127—1491no—
95#127—1491no—
96#124—1491no—
97#124—1491no—
98#121—2982no—
99#120—2982no—
100#117#1059701011yescharacteristic, complemented
101C2×C22⋊C4—2982no—
102#99—2982no—
103#99—1494no—
104C24—1492no—
105#41—5962no—
106C2×Q8—1491no—
107C2×D4—2982no—
108C2×D4—2982no—
109C2×D4—2981no—
110C2×D4—5962no—
111C2×D4—1492no—
112C2×D4—1491no—
113C2×D4—1491no—
114C2×D4—1491no—
115C22×C4—2981no—
116C22×C4—5962no—
117C22×C4C2×#1059701011yescharacteristic
118C4⋊C4—21no—
119C22⋊C4—21no—
120C22⋊C4—2982no—
121C22⋊C4—2982no—
122C22⋊C4—2984no—
123C22⋊C4—5962no—
124C42C2×#1059701011yescharacteristic, complemented
125C42C2×#1059701011yescharacteristic, complemented
126C23—2982no—
127C23—2982no—
128C23—2981no—
129C23—1492no—
130C23—1492no—
131C23—11922no—
132C23C22⋊#1059701011yescharacteristic
133Q8—5961no—
134D4—5962no—
135D4—5961no—
136D4—5961no—
137D4—5961no—
138D4—5962no—
139D4—11922no—
140D4—11922no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—2981no—
145C2×C4—5962no—
146C2×C4—5964no—
147C2×C4—11924no—
148C2×C4C22⋊#1059701011yescharacteristic
149C2×C4C22×#1059701011yescharacteristic
150C22—41no—
151C22—2982no—
152C22—2982no—
153C22—5962no—
154C22—5962no—
155C22—5964no—
156C22—5962no—
157C22—5961no—
158C22—11922no—
159C22#1801197012yes—
160C22C2×C22⋊#1059701011yescharacteristic
161C4—21no—
162C4—21no—
163C4—41no—
164C4—41no—
165C4—5961no—
166C4—11924no—
167C2—21no—
168C2—22no—
169C2—5962no—
170C2—5962no—
171C2—11921no—
172C2C2×#1801197011yescharacteristic
subgroupG/H
centerC2C2×#18011970
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#117×C149C4
socleC2×C149C2×#99
prime radical#23750194C2
cosocleC2×D596C23
hypercenter#117#10597010
hypocenterC149#2127
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#18011970C2semidirect
2. #23750532C2semidirect
3. #23750530C2semidirect
8. C2×#14558736C4semidirect
10. #18011908C4semidirect
12. #18011899C4semidirect
16. #117×C149C4semidirect
22. C2×Dic298C2×C4semidirect
27. C2×D596C2×C4semidirect
37. C42×C149C2×C4semidirect
38. C42×C149C2×C4semidirect
86. C149#2127semidirect
100. #117#10597010semidirect
124. C42C2×#10597010semidirect
125. C42C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119702
#237505322
#237505302
#237501942
#2127149