Finite Group Databasebeta

← #34060864

Subgroups — #34060864

Order 19072.

280 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 92 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×C4⋊#11924753C211yesmaximal, characteristic
2C2×#18011966C211yesmaximal, characteristic
3#23750491C212yesmaximal
4#23750491C212yesmaximal
5C2×#18011876C211yesmaximal, characteristic
6C22×#11924753C2212yes—
7C22×#11924753C2212yes—
8C4⋊#11924753—22no—
9#18011966—22no—
10C22×Dic298C411yescharacteristic
11#18011876—22no—
12#18011876—22no—
13C2×#14558715C411yescharacteristic
14C2×#14558715C411yescharacteristic
15C2×C4×Dic149C2211yescharacteristic
16C2×C4×Dic149C2211yescharacteristic
17C2×C4×Dic149C2211yescharacteristic
18C2×C4⋊C4×C149C411yescharacteristic
19C2×#11924753—22no—
20C2×#11924753—22no—
21C2×#11924753—22no—
22C2×#11924753—24no—
23C2×#11924753Q814yescomplemented
24C2×Dic298—22no—
25C2×Dic298—22no—
26C2×Dic298—22no—
27C22×Dic149C2×C411yescharacteristic
28C22×Dic149C2×C411yescharacteristic
29C22×Dic149C2×C411yescharacteristic
30C22×Dic149C2311yescharacteristic
31#14558715—22no—
32#14558715—22no—
33C4×Dic149—21no—
34C4×Dic149—21no—
35C4×Dic149—21no—
36C4×Dic149—21no—
37C4×Dic149D412yes—
38C4×Dic149D412yes—
39C22×C4×C149C2×C411yescharacteristic
40C22×C4×C149C2×C411yescharacteristic
41C22×C4×C149C2×C411yescharacteristic
42C4⋊C4×C149—22no—
43#11924753—24no—
44#11924753—42no—
45Dic298—28no—
46C2×Dic149—21no—
47C2×Dic149—21no—
48C2×Dic149—21no—
49C2×Dic149—21no—
50C2×Dic149—21no—
51C2×Dic149—22no—
52C2×Dic149C22⋊C412yes—
53C2×Dic149M1612yes—
54C2×Dic149C2×D411yescharacteristic
55C2×Dic149C2×D411yescharacteristic
56C2×Dic149C2×Q812yes—
57C2×Dic149#4112yes—
58C23×C149C22×C411yescharacteristic
59C2×C4×C149—21no—
60C2×C4×C149—21no—
61C2×C4×C149—22no—
62C2×C4×C149—21no—
63C2×C4×C149—22no—
64C2×C4×C149C22⋊C412yes—
65C2×C4×C149M1612yes—
66C22×C149C2×C22⋊C411yescharacteristic
67C22×C149C4×Q812yes—
68C22×C149C2×M1611yescharacteristic
69C22×C149C2×M1611yescharacteristic
70C22×C149#13112yes—
71C4×C149—22no—
72C4×C149—22no—
73C4×C149—41no—
74Dic149—22no—
75Dic149—22no—
76Dic149—41no—
77Dic149C22⋊Q812yes—
78Dic149#12411yescharacteristic
79Dic149C4⋊Q811yescharacteristic
80C2×C149#39111yescharacteristic
81C2×C149#40711yescharacteristic
82C2×C149#40811yescharacteristic
83C2×C149#44612yes—
84C2×C149#44612yes—
85C149#198511yescharacteristic, complemented, Sylow
86#1985—1491nomaximal, Sylow
87C2×C4×Q8—1491no—
88C2×C4⋊C8—1491no—
89C2×#97—1491no—
90#336—1492no—
91#336—1492no—
92C22×Q8—1491no—
93C22×C8—1492no—
94C22×C8—1492no—
95C4×Q8—2982no—
96C4×Q8—2982no—
97C2×C4⋊C4—1491no—
98C2×C4⋊C4—1491no—
99C2×C4⋊C4#1059701011yescharacteristic
100C2×C42—1491no—
101C2×C42—1491no—
102C2×C42—1491no—
103C4⋊C8—2982no—
104#97—2982no—
105C2×Q8—2982no—
106C2×Q8—2982no—
107C2×Q8—2982no—
108C22×C4—1491no—
109C22×C4—1491no—
110C22×C4—1491no—
111C22×C4—1491no—
112C22×C4C2×#1059701011yescharacteristic
113C22×C4C2×#1059701011yescharacteristic
114C22×C4C2×#1059701011yescharacteristic
115C2×C8—2982no—
116C2×C8—2982no—
117C2×C8—2982no—
118C2×C8—2984no—
119C2×C8—1494no—
120C4⋊C4—22no—
121C4⋊C4—2982no—
122C4⋊C4—2982no—
123C42—2981no—
124C42—2981no—
125C42—2981no—
126C42—2981no—
127C42—1492no—
128C42—1492no—
129C23C22×#1059701011yescharacteristic
130Q8—2988no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—2981no—
137C2×C4—2981no—
138C2×C4—2981no—
139C2×C4—2981no—
140C2×C4—2981no—
141C2×C4—2982no—
142C2×C4—1492no—
143C2×C4—1492no—
144C2×C4—1491no—
145C2×C4—1491no—
146C2×C4—1492no—
147C2×C4—1492no—
148C2×C4C22⋊#1059701012yes—
149C2×C4#1455874612yes—
150C8—2984no—
151C8—5962no—
152C22C2×C22⋊#1059701011yescharacteristic
153C22Q8×#1059701012yes—
154C22D149⋊M1611yescharacteristic
155C22C2×#1455874611yescharacteristic
156C22#1801199812yes—
157C4—22no—
158C4—22no—
159C4—41no—
160C4—2982no—
161C4—2982no—
162C4—5961no—
163C4—1492no—
164C4—1491no—
165C4—1491no—
166C2(C2×#10597010)⋊Q811yescharacteristic
167C2#2375059611yescharacteristic
168C2#2375059811yescharacteristic
169C2#2375067512yes—
170C2#2375067712yes—
subgroupG/H
center, FrattiniC23C22×#10597010
commutator, socle, prime radicalC23×C149C22×C4
FittingC2×C4⋊C4×C149C4
cosocleC22×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1985
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
23. C2×#11924753Q8semidirect
85. C149#1985semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#119247532
C2×#180119662
#237504912
C2×#180118762
#1985149